revisi matrik.docx

8/17/2019 revisi matrik.docx

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Invers 2x2

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[CODE]

Public Function Det22(Matrix()) As Boolean

Di A As !on"

Di B As !on"Di C As !on"

Di # As !on"

A $ Matrix(%& %)

B $ Matrix(%& 2)

C $ Matrix(2& %)

# $ Matrix(2& 2)

I' (A #) (B C) $ * +,en

Det22 $ False

Else

Det22 $ +rue

En# I'

En# Function

Public Function -Det22(Matrix()) As Double

Di A As !on"

Di B As !on"

Di C As !on"

Di # As !on"

A $ Matrix(%& %)

B $ Matrix(%& 2)

C $ Matrix(2& %)# $ Matrix(2& 2)

-Det22 $ (A #) (B C)

En# Function

[.CODE]

______________________________________________________________

Invers /x/

______________________________________________________________

[CODE]

Public Function Det//(Matrix()) As Boolean

Di A%% As !on"

Di A%2 As !on"Di A%/ As !on"

Di A2% As !on"

Di A22 As !on"

Di A2/ As !on"

Di A/% As !on"

Di A/2 As !on"

Di A// As !on"

Di -alue As Double

A%% $ Matrix(%& %)

A%2 $ Matrix(%& 2)

A%/ $ Matrix(%& /)

A2% $ Matrix(2& %)


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A22 $ Matrix(2& 2)

A2/ $ Matrix(2& /)

A/% $ Matrix(/& %)

A/2 $ Matrix(/& 2)

A// $ Matrix(/& /)

0Aturan 1arrus-alue $ (A%% A22 A//) (A%2 A2/ A/%) (A%/ A2% A/2) (A/% A22

A%/) (A/2 A2/ A%%) (A// A2% A%2)

I' -alue $ * +,en

Det// $ False

Else

Det// $ +rue

En# I'

En# Function

Public Function -Det//(Matrix()) As Double 0Mencari Deterinan atri3s / x / #"n

Aturan 1arrus

Di A%% As !on"

Di A%2 As !on"

Di A%/ As !on"

Di A2% As !on"

Di A22 As !on"

Di A2/ As !on"

Di A/% As !on"

Di A/2 As !on"

Di A// As !on"

A%% $ Matrix(%& %)

A%2 $ Matrix(%& 2)A%/ $ Matrix(%& /)

A2% $ Matrix(2& %)

A22 $ Matrix(2& 2)

A2/ $ Matrix(2& /)

A/% $ Matrix(/& %)

A/2 $ Matrix(/& 2)

A// $ Matrix(/& /)

-Det// $ (A%% A22 A//) (A%2 A2/ A/%) (A%/ A2% A/2) (A/% A22

A%/) (A/2 A2/ A%%) (A// A2% A%2)

En# Function

[.CODE]

1al a4li3asi

Permasalahan ini berawal dari tugas Aljabar Linear. Mumpung nganggur aku coba nyicil ngerjain dikit".Kesusahan ngetik matriks yang berordo 4x4. Aku bngung co d Ms.!ord #$# cuman bisa buat matriks ordomaksimal %x% di &'uation &ditor.

(etelah utak katik. . . .akhirnya ' temuin jg caranya. )egini caranya*+ara membuat matrik berordo 4x4

$. Klik menu insert lalu pilih &'uation ,untuk -ile yang tersimpan pada word compatibility mode/ alias pengsa0e1an pada word 231##% maka sa0e dulu menjadi #$# atau ##3


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. Klik option matrik

%. )uat dulu matriks berordo x yang menggunakan kurung4. Klik salah satu komponen di dalam matriks terserah yang mana. Lalu klik pada option matrik %x$

5. 6asilnya seperti ini lakukan langkah yang sama untuk elemen matrik yang lainnya

7. 6asilnya seperti ini

3. 8empatkan kursor sebelah kanan elemen matrik ,di dalam kurung9 lalu beri spasi sesuai jarak antara elemen


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:. Matrik blok;sorot matrik tersebut,semua elemen dalam kurung9 lalu copi dan paste dan tempatkan hasilsalinnya pada posisi ,kursosr9 yang telah di beri spasi

2. Lalu input;ketik dech angka matrik yang kita inginkan

$#. ow +olumn and ?umerial yang disatukan dalam sebuahsimbol matriks ,119

contoh pengolahan matriks ordo 4x4Mencari Minor, Cofaktor, Adjoin, Deterinan dan In!er" #ada atrik" ordo 4 $ 4


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@iposkan oleh anggi setiawan di $4.54 % komentar* Kirimkan ni lewat &mail )log8hisB )erbagi ke 8witter)erbagi ke Cacebook)agikan ke Pinterest

)eranda

Langganan* &ntri ,Atom9

%AM

MEN&ENAI SA'A

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an((i "etia)an Lihat pro-il lengkapku

ARSI* B+O&

• D #$4 ,$9

o D ?o0ember ,$9

Matriks tersusun atas >ow +olumn and ?umerial yan...

8emplate Picture !indow. @iberdayakan oleh )logger .

Math ( )eauti-ul

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• Tukar Link

(&P 13#$

Menghitung @eterminan Matriks Menggunakan Ko-aktor

() *otes

Pada tulisan ini saya akan membagikan sidikit ilmu yang saya dapat tentang

bagaimana cara menghitung determinan matriks. Metode yang digunakan adalah

menggunakan Ekspansi Kofaktor. Metode ini tidak hanya digunakan untuk

menghitung determinan matriks atau tapi digunakan untuk matriks

yang berordo lebih besar lagi seperti, dan seterusnya. Untuk

menghitung determinan menggunakan metode ini, rumusnya dijamin

oleh Teorema berikut.

Teorema 1.

Determinan matriks yang berukuran dapat dihitung dengan mengalikan entri-entri dalam

suatu baris (atau kolom) dengan kofaktor-kofaktornya dan menambahkan hasil-hasil kali yang

dihasilkan yakni untuk setiap dan , maka

det(A) = a1jC 1j + ajC j + ! + anjC nj

(ekspansi kofaktor sepanjang kolom ke-j)

atau

det(A) = ai1C i1 + aiC i + ! + ainC in

https://aimprof08.wordpress.com/tukar-link/https://aimprof08.wordpress.com/tukar-link/


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(ekspansi kofaktor sepanjang baris ke-i)

Untuk lebih memperjelas apa itu kofaktor, perhatikan Definisi dibawah ini.

Definisi 2.

"ika A adalah matriks kuadrat, maka minor entri aij dinyatakan oleh # ij dan didefinisikan menjadi

determinan submatriks yang tetap setelah baris ke-i dan kolom ke-j di$oret dari A% &ilangan (-

1)i+j # ijdinyatakan oleh C ij dan dinamakan kofaktor entri aij .

Contoh 3.

Misalkan kita punya matriks A = . Tentukan minor entri a11, a12,

dan a13. Tentukan juga kofaktor entri M11, M12 dan M13

Penyelesaian.

minor entri a11 adalah M11 = = = !"#$ % &"'$ = ('

kofaktor a11 adalah )11 = "*($1+1M11 = "*($2"('$ = ('

minor entri a12 adalah M12 = = = +"#$ % ("'$ = (

kofaktor a12 adalah )12 = "*($1+2M12 = "*($3"($ = *(

minor entri a13 adalah M13 = = = +"&$ % ("!$ = -


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kofaktor a13 adalah )13 = "*($1+3M13 = "*($4"-$ = -

Contoh 4.

ari Contoh 1 diatas, tentukan determinan matriks A

Penyelesaian.

Menggunakan yang diberikan pada Teorema diatas dengan mengambil i = ( dan j

= (, +, dan -, maka diperoleh.

det"A$ = a11)11 / a12)12 / a13)13

= -"('$ / ("*($ / "*&$"-$

= % ( % (+

= +'

Contoh 5.

Tentukan determinan matriks A =

Penyelesaian.

Menggunakan yang diberikan pada Teorema diatas dengan mengambil i = - dan j

= (, +, dan -, maka diperoleh.

det"A$ =


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= a31)31 / a32)32 / a33)33

= a31"*($3+1M31 / a32"*($3+2M31 / a33"*($3+3M31

= a31M31 % a32M31 / a33M31

= - % + / +

= -0'"#$*"'$1 % +0"#$*#"$1 / +0"'$*#"'$1

= (&& % % 2'

=

atau jika ingin lebih cepat, kita bisa melihat entri yang mengandung nol

agar lebih mempersingkat waktu mengerjakan. 3arena dalam baris pertama

terdapat dua entri nol, maka i = ( dan j = (, +, - kemudian gunakan rumus.

det"A$ = a11)11 / a12)12 / a13)13

= a11"*($1+1M11 / a12"*($1+2M12 / a13"*($1+3M13

= a11M11 % a12M12 / a13M13

= % ' /

= % '0#"+$*#"-$1 /

=

Contoh 6.


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Tentukan determinan matriks 4 =

Penyelesaian.

dengan menggunakan kolom pertama pada matriks 4 sebagai kofaktor dan

berdasarkan Teorema diatas dengan mengambil i = (, +, -, & dan j = ( maka

diperoleh.

det"4$ =

= a11)11 / a21)21 / a31)31 / a41)41

= a11"*($1+1M11 / a21"*($2+1M21 / a31"*($3+1M31 / a41"*($4+1M41

= a11M11 % a21M21 / a31M31 % a41M41

= + % ( / %

hitung lagi determinan untuk matriks -5- nya

= +0ambil i = ( dan j = (, +, -1 % (0ambil i = (, +, - dan j = -1

6untuk matriks ketiga dan keempat tidak perlu dihitung karena

koefesiennya , sehingga apabila dikali, hasilnya akan tetap = 7

= +0a11)11 / a12)12 / a13)131 % (0a13)13 / a23)23 / a33)331 / %

= +0a11"*($1+1M11 / a12"*($1+2M12 / a13"*($1+3M131 % (0a13"*($1+3M13 / a23"*($2+3M23 /

a33"*($3+3M331

= +0a11M11 % a12M12 / a13M131 % (0a13M13 / a23M23 / a33M331


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= +" % ( / ( $ % ("( % / - $

= +"0("-$*+"$1 % (0+"-$*("$1 / (0+"+$*("($1$ % ("(0+"+$*("($1 %

0("+$*("-$1 / -0("($*+"-$1$

= +" % ' / -$ % ("- % / -"*!$$

= *' / (+

= '

Contoh 7.

Tentukan determinan matriks

Penyelesaian.

8elanjutnya, 3arena dan merupakan determinan ,

maka kita uraikan lagi dengan menggunakan kofaktor. Ambil

dan .

engan menggunkaan Metode Sarrus, diperoleh

https://aimprof08.wordpress.com/2015/12/06/metode-sarrus/https://aimprof08.wordpress.com/2015/12/06/metode-sarrus/


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9adi, diperoleh

Sumber : Anton, ;., (22+, Aljabar 'inier lementer ,


19/44

Sare ti"-

• Face%ook -

• T$itter

• !oo+le

• etak

• Simpan Se%a+ai P0F

•

Terkait

Menghitung Determinan Menggunakan Eselon Barisdalam "Aljabar"

Determinan Matriks dengan Metode CH!dalam "Aljabar"

Metode arrusdalam "Aljabar"

B" aimpro123 4 Posted in Al5a%ar 4 Ta++ed determinan6 determinan matriks6 determinan matriks

(7(6 ko1aktor6 matriks

83

9avi+asi pos

'nterpolasi 9e$ton

Aturan Simpson - per : ;:<

83 comments on =Men+>itun+ 0eterminan MatriksMen++unakan Ko1aktor?

omment navi+ation

9e$er comments @

-. mojang priangan tea

OKTOBER 8, 2012 -28- AM

untuk ordo 4#4 n$a mana%%

BALAS

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aimpro123

OKTOBER 8, 2012 :2 PM

silahkan diba&a' sudah ditambahkan utk &ontoh matriks 4#4 n$a

BALAS

. neneng

OKTOBER 19, 2012 -3 PM

msh kurng (aham ma rumus 4#4

BALAS

aimpro123

OKTOBER 20, 2012 88 AM

bagaian mana $ang belum di(ahami%

determinan 4#4 ini ado(si ato (ngembangan dari 3#3' jadi sblumn$a &oba ngertiin $ang 3#3 trlebih

dahulu

BALAS

:. hilda

OKTOBER 24, 2012 (8( PM

assalam)*r)*b)) share donk)) a(a $g dimaksud dengan men&ari determinan dengan &ara langsung%% di bukun$a

ada soal n$ari determinan dengan &ara sarus' koaktor' eselon baris' obe' dan &ara langsung) ,ah $g sa$a g t*

tuh dengan &ara langsung)) a((a $aa maksudn$a%%

trims

BALAS

aimpro123

OKTOBER 24, 2012 C8- PM

*aalaikumslams$a juga baru dnger ni

klo boleh t* da(at dri buku mana -determinan dengan &ara langsung. %

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BALAS

(. Sapta Dadi

NOVEMBER 11, 2012 -2-C PM

sangat bermanaat'terimakasih

BALAS

8. est" $ulansari ;est"Ee+"<

NOVEMBER 12, 2012 -82 PM

setelah sa$a teliti'kok hasiln$a beda $a antara &ara eselon dengan koaktor (adahal angkan$a sama % mohon

saran)

BALAS

aimpro123

NOVEMBER 12, 2012 88- PM

kalo boleh tahu' &ontoh $g mana $ %

BALAS

est" $ulansari ;est"Ee+"<

NOVEMBER 13, 2012 --8 AM

&ontoh $ang menghhiung determinan B antara menggunakan &ara koaktor dengan artikel

anda $ang menghitung determinan dengan &ara eselon baris hasiln$a kok berbeda% kalo

koaktor hasiln$a /) ta(i klo eselon hasiln$a 120 mohon (en&erahann$a)terimakasih

BALAS

aimpro123

NOVEMBER 13, 2012 -2:) PM

oh i$a' baru sadar juga

dsana salah di !BE (ertama - -' seharusn$a - -) arena

kalo (ake ' ini mengakibatkan determiann$a 2 kali dari matriks

a*al ba&a dihtt(s00aim(ro5)*ord(ress)&om02120601/0siat7siat7

determinan7matriks0' siat no)38

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BALAS

Minami Kuro

NOVEMBER 14, 2012 (2 AM

itu bagian $ang mana $a mas% sa$a kurang (aham nih 797

BALAS

aimpro123

NOVEMBER 14, 2012 --2 AM

ini membhas mslah &ontoh $g ada ditulisn ini &ontoh 48

dengan &ontoh di Menghitung Determinan

Menggunakan Eselon Baris &ontoh 28

BALAS

est" $ulansari ;est"Ee+"<

NOVEMBER 14, 2012 -:2 PM

masih bingung mas))heehe

BALAS

aimpro123

NOVEMBER 14, 2012 -2( PM

jika kita melakukan !BE (ada suatu matriks maka

determinan matriks tersebut akan berubah jika kedua

baris di(ertukarkan atau kita kali suatu baris matriks

dengan skalar

ba&ahtt(s00aim(ro5)*ord(ress)&om02120601/0siat7

siat7determinan7matriks0 8

nah (ada &ontoh ditulisan sa$a itu

htt(s00aim(ro5)*ord(ress)&om0212060140menghitu

ng7determinan7menggunakan7eselon7baris0 8' dsana kan

s$a (ake o(erasi -baris kedua 2:B2 ; B1.' o(erasi B? @ 1202 @ /

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BALAS

/) PIN!"#$IK% Men&ari olusi ersamaan Menggunakan Aturan Cramer Math Beautiul

. anictk

DESEMBER 28, 2012 -2 AM

untuk determinan matrik dengan ordo 44 untuk men&ari minor bagaimana &aran$a% a(akah menggunakan

metode sarrus%%%%

BALAS

aimpro123

DESEMBER 28, 2012 8:C PM

sama &aran$a dgn ordo 3#3 s(rti &ontoh soal diatas

BALAS

3. Melinda Tresna$ati

JANUARI 20, 2013 -2C PM

mau nan$a kalo ordo 4 4 a(a ga bisa (ake &ara MA $ang (ake minor itu% terimakasih

BALAS

omment navi+ation

9e$er omments @

Berikan Baa!an

(elamat @atang di )log E

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24/44

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25/44

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Persamaan !aris Sin++un+ Lin+karan ;-< Kenapa #umla> Sisi Te+ak Se+iti+a Siku,Siku Le%i> Pan5an+ dari Sisi Mirin+H

Langganan

https://aimprof08.wordpress.com/2016/04/25/pembahasan-tpa-usm-stan-2015-1/https://aimprof08.wordpress.com/2016/04/24/sifat-ruang-vektor/https://aimprof08.wordpress.com/2016/04/21/ring/https://aimprof08.wordpress.com/2016/04/18/ruang-vektor/https://aimprof08.wordpress.com/2016/04/16/pembahasan-tpa-deret-usm-stan-2013/https://aimprof08.wordpress.com/2016/04/15/pembuktian-volume-limas/https://aimprof08.wordpress.com/2016/04/12/aturan-kosinus/https://aimprof08.wordpress.com/2016/04/10/pembahasan-tpa-usm-stan-2013-5/https://aimprof08.wordpress.com/2016/04/08/lingkaran-luar-segitiga/https://aimprof08.wordpress.com/2016/04/05/garis-singgung-persekutuan-dalam-dua-lingkaran/https://aimprof08.wordpress.com/2016/04/03/pembahasan-tpa-usm-stan-2013-4/https://aimprof08.wordpress.com/2016/04/03/try-out-sbmptn-bersama/https://aimprof08.wordpress.com/2016/04/01/lingkaran-dalam-segitiga/https://aimprof08.wordpress.com/2016/03/28/garis-singgung-persekutuan-luar-dua-lingkaran/https://aimprof08.wordpress.com/2016/03/26/pembahasan-tpa-usm-stan-2013-3/https://aimprof08.wordpress.com/2016/03/25/bekerja-bersama-sama/https://aimprof08.wordpress.com/2016/03/23/pembahasan-tpa-usm-stan-2013-2/https://aimprof08.wordpress.com/2016/03/22/persamaan-kuadrat/https://aimprof08.wordpress.com/2016/03/20/pembahasan-tpa-usm-stan-2013-1/https://aimprof08.wordpress.com/2016/03/18/isomorfisma-grup/https://aimprof08.wordpress.com/2016/03/14/homomorfisma-natural/https://aimprof08.wordpress.com/2016/03/10/kernel-dan-image-homomorfisma-grup/https://aimprof08.wordpress.com/2016/03/06/persamaan-garis-singgung-lingkaran-2-2/https://aimprof08.wordpress.com/2016/03/02/persamaan-garis-singgung-lingkaran-1/https://aimprof08.wordpress.com/2016/02/27/kenapa-jumlah-sisi-tegak-segitiga-siku-siku-lebih-panjang-dari-sisi-miring/https://aimprof08.wordpress.com/2016/02/27/kenapa-jumlah-sisi-tegak-segitiga-siku-siku-lebih-panjang-dari-sisi-miring/https://aimprof08.wordpress.com/2016/04/25/pembahasan-tpa-usm-stan-2015-1/https://aimprof08.wordpress.com/2016/04/24/sifat-ruang-vektor/https://aimprof08.wordpress.com/2016/04/21/ring/https://aimprof08.wordpress.com/2016/04/18/ruang-vektor/https://aimprof08.wordpress.com/2016/04/16/pembahasan-tpa-deret-usm-stan-2013/https://aimprof08.wordpress.com/2016/04/15/pembuktian-volume-limas/https://aimprof08.wordpress.com/2016/04/12/aturan-kosinus/https://aimprof08.wordpress.com/2016/04/10/pembahasan-tpa-usm-stan-2013-5/https://aimprof08.wordpress.com/2016/04/08/lingkaran-luar-segitiga/https://aimprof08.wordpress.com/2016/04/05/garis-singgung-persekutuan-dalam-dua-lingkaran/https://aimprof08.wordpress.com/2016/04/03/pembahasan-tpa-usm-stan-2013-4/https://aimprof08.wordpress.com/2016/04/03/try-out-sbmptn-bersama/https://aimprof08.wordpress.com/2016/04/01/lingkaran-dalam-segitiga/https://aimprof08.wordpress.com/2016/03/28/garis-singgung-persekutuan-luar-dua-lingkaran/https://aimprof08.wordpress.com/2016/03/26/pembahasan-tpa-usm-stan-2013-3/https://aimprof08.wordpress.com/2016/03/25/bekerja-bersama-sama/https://aimprof08.wordpress.com/2016/03/23/pembahasan-tpa-usm-stan-2013-2/https://aimprof08.wordpress.com/2016/03/22/persamaan-kuadrat/https://aimprof08.wordpress.com/2016/03/20/pembahasan-tpa-usm-stan-2013-1/https://aimprof08.wordpress.com/2016/03/18/isomorfisma-grup/https://aimprof08.wordpress.com/2016/03/14/homomorfisma-natural/https://aimprof08.wordpress.com/2016/03/10/kernel-dan-image-homomorfisma-grup/https://aimprof08.wordpress.com/2016/03/06/persamaan-garis-singgung-lingkaran-2-2/https://aimprof08.wordpress.com/2016/03/02/persamaan-garis-singgung-lingkaran-1/https://aimprof08.wordpress.com/2016/02/27/kenapa-jumlah-sisi-tegak-segitiga-siku-siku-lebih-panjang-dari-sisi-miring/


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Persamaan Lin+karan

Domomorfsma !rup

!rup Faktor

Si1at,Si1at Su%+rup 9ormal

Su%+rup 9ormal

Teorema La+ran+e

Les Privat Matematika

Koset

Si1at,Si1at !rup Siklik

!rup Siklik

!a%un+an6 'risan dan Perkalian Su%+rup

Mem%uat Ta%el den+an LaTeI

0eterminan Matriks den+an Metode D'G

Berapa #umla> Se+i Ti+aH

Metode Sarrus

Mele$ati Titik den+an Maksimal !aris

Menulis 0ocument den+an LaTeI

Tanpa Mele$ati Sisi "an+ Sama

Ba+aimana Menentukan Bilan+an Prima H ;<

Karakteristik Su%+rup

Su%+rup

Si1at,Si1at !rup

Keter%a+ian

Komposisi Fun+si ;<

Ba+aimana Menentukan Bilan+an Prima H ;-<

Kon+ruensi Modulo ;<

Kon+ruensi Modulo ;-<

Akar suatu Bilan+an

TPA SBMPT9 2-

TPA SBMPT9 2-( ;<

TPA SBMPT9 2-(

Pem%a>asan TPA USM STA9 2-( ;:<

Pem%a>asan Matematika U9 SMA 2-8 ;(<

Pem%a>asan Matematika U9 SMA 2-8 ;:<

Pem%a>asan Matematika U9 SMA 2-8 ;<

Pem%a>asan Matematika U9 SMA 2-8 ;-< Pem%a>asan Matematika U9 SMA 2-: ;(<

Pem%a>asan Matematika U9 SMA 2-: ;:<

Pem%a>asan Matematika U9 SMA 2-: ;<

Pem%a>asan Matematika U9 SMA 2-: ;-<

Pem%a>asan TPA 0eret S9MPT9 2-- ;Kode Soal :<

Pem%a>asan TPA Matematika S9MPT9 2-- ;Kode Soal :<

Matriks 'nvers Ter+eneralisasi

Apa itu Matriks 'nvers Ter+eneralisasi H

Pem%a>asan Matematika U9 SMA 223 ;(<

Pem%a>asan Matematika U9 SMA 223 ;:< Pem%a>asan Matematika U9 SMA 223 ;


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Pem%a>asan Matematika U9 SMA 223 ;-<

Men++anti Gutput pada LaTeI

Kenapa P0F,I>an+e H

Pem%a>asan TPA USM STA9 0''' 2-( ;<

Pem%a>asan TPA USM STA9 0''' 2-( ;-<

2J2 tak terdefnisi H

Pem%a>asan Matematika U9 SMA 2-( ;(<

Pem%a>asan Matematika U9 SMA 2-( ;:<

ara 'nstall LaTeI

Pem%a>asan Matematika U9 SMA 2-( ;<

Luas Se+iempat Sem%aran+

Pem%a>asan Matematika U9 SMA 2-( ;-<

Pem%a>asan Matematika U9 SMA 2- ;(<

Pem%a>asan Matematika U9 SMA 2- ;:<

Pem%a>asan Matematika U9 SMA 2- ;-<

LaTeI 1or Face%ook

Pem%a>asan Matematika U9 SMA 2-- ;(<

Pem%a>asan Matematika U9 SMA 2-- ;:<

Pem%a>asan Matematika U9 SMA 2-2 ;(<

Mo>on Maa1

Pem%a>asan Matematika U9 SMA 2-2 ;:<

Pem%a>asan Matematika U9 SMA 2-2 ;<

Pem%a>asan Matematika U9 SMA 2- ;<

Pem%a>asan Matematika U9 SMA 2-2 ;-<

Teori !rup

Pem%a>asan Matematika U9 SMA 22C ;(<

Pem%a>asan Matematika U9 SMA 22C ;:<

Menulis &uation pada Blo+spot

Pem%a>asan Matematika U9 SMA 22C ;<

Pem%a>asan Matematika U9 SMA 22C ;-<

Akses #urnal !ratis

Pem%a>asan Matematika U9 SMA 22 ;:<

Pem%a>asan Matematika U9 SMA 22 ;<

Pem%a>asan Matematika U9 SMA 22 ;-<

'nvers Matriks den+an a"le",Damilton

Pro%lem ;:< 'nte+ral Tri+onometri Pem%a>asan &ksponen dan Lo+aritma U9 SMA ;(<

7 tan 7 -

Du%un+an Fun+si !amma dan Beta

'nte+ral dari 'nvers Fun+si Tri+onometri

Luas Kurva 0istri%usi 9ormal

Da%is 0i%a+i -:

Pro%lem ;:< 'nte+ral

Persamaan !aris Sin++un+ Lin+karan ;<

Si1at,Si1at Lo+aritma 9atural

- Turunan dari 'nvers Fun+si Tri+onometri

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un-sma-2012-1/https://aimprof08.wordpress.com/2014/04/30/latex-for-facebook/https://aimprof08.wordpress.com/2014/04/19/pembahasan-matematika-un-sma-2011-4/https://aimprof08.wordpress.com/2014/04/15/pembahasan-matematika-un-sma-2011-3/https://aimprof08.wordpress.com/2014/04/14/pembahasan-matematika-un-sma-2010-4/https://aimprof08.wordpress.com/2014/04/13/mohon-maaf/https://aimprof08.wordpress.com/2014/04/12/pembahasan-matematika-un-sma-2010-3/https://aimprof08.wordpress.com/2014/04/08/pembahasan-matematika-un-sma-2010-2/https://aimprof08.wordpress.com/2014/04/05/pembahasan-matematika-un-sma-2012-2/https://aimprof08.wordpress.com/2014/04/04/pembahasan-matematika-un-sma-2010-1/https://aimprof08.wordpress.com/2014/04/03/teori-grup/https://aimprof08.wordpress.com/2014/03/14/pembahasan-matematika-un-sma-2009-4/https://aimprof08.wordpress.com/2014/03/10/pembahasan-matematika-un-sma-2009-3/https://aimprof08.wordpress.com/2014/03/06/menulis-equation-pada-blogspot/https://aimprof08.wordpress.com/2014/03/06/pembahasan-matematika-un-sma-2009-2/https://aimprof08.wordpress.com/2014/03/02/pembahasan-matematika-un-sma-2009-1/https://aimprof08.wordpress.com/2014/03/02/akses-jurnal-gratis/https://aimprof08.wordpress.com/2014/02/20/pembahasan-matematika-un-sma-2007-3/https://aimprof08.wordpress.com/2014/02/15/pembahasan-matematika-un-sma-2007-2/https://aimprof08.wordpress.com/2014/02/11/pembahasan-matematika-un-sma-2007-1/https://aimprof08.wordpress.com/2014/01/23/invers-matriks-dengan-cayley-hamilton/https://aimprof08.wordpress.com/2013/12/23/problem-23-integral-trigonometri/https://aimprof08.wordpress.com/2013/12/08/pembahasan-eksponen-dan-logaritma-un-sma-4/https://aimprof08.wordpress.com/2013/10/27/x-tan-x-1/https://aimprof08.wordpress.com/2013/09/13/hubungan-fungsi-gamma-dan-beta/https://aimprof08.wordpress.com/2013/09/08/integral-dari-invers-fungsi-trigonometri/https://aimprof08.wordpress.com/2013/09/03/luas-kurva-distribusi-normal/https://aimprof08.wordpress.com/2013/09/01/habis-dibagi-13/https://aimprof08.wordpress.com/2013/08/31/problem-23-integral/https://aimprof08.wordpress.com/2013/08/30/persamaan-garis-singgung-lingkaran-2/https://aimprof08.wordpress.com/2013/08/25/sifat-sifat-logaritma-natural/https://aimprof08.wordpress.com/2013/08/22/1-2/https://aimprof08.wordpress.com/2013/08/18/turunan-dari-invers-fungsi-trigonometri/


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9ilai Lo+ ;2<

Fun+si !amma

0eret MacLaurin

'nte+ral lo+ 76 ln 76 dan eJ7

turunan 7JN7J;7 iemann

!aris Berat Se+iti+a

#umla> 0eret K>usus

*olume Bola den+an 'nte+ral Lipat Ti+a

Limit Tri+onometri Kasus K>usus

Men+>itun+ Akar den+an Dampiran Turunan

Pem%a>asan Matematika 0asar S'MAK U' 2- NKode Soal -O ;<

Pem%a>asan Matematika 0asar S'MAK U' 2- NKode Soal -O ;-<

Pro%lem ;<

Pro%lem ;-< Tin++i Se+iti+a

Pem%a>asan Matematika 0asar SBMPT9 2-: NKode Soal -O

Pem%a>asan 0eret TPA SBMPT9 2-: ;Kode Soal --<

Pem%a>asan TPA SBMPT9 2-: ;Kode Soal --<

Pro%lem;2< Tri+onometri

Topi Ulan+ Ta>un

Mem%uat &lips

Kumpulan Soal Test Matematika U!M Pascasar5ana

Pro%lem ;-C< Persamaan 0i1erensial

Pem%a>asan Potensi Akademik Pacasar5ana NPAPsO ;<

Pem%a>asan Potensi Akademik Pacasar5ana NPAPsO ;-<

Kumpulan Soal S'MAK U'

Kumpulan Soal UMPT9 / SPMB / S9MPT9

Kumpulan Soal U5ian 9asional SMA

Pen"elesaian Persamaan Linier Grde - Metode Faktor 'nte+ral

Pen"elesaian Persamaan 0i1erensial P0 Tidak &ksak ;Faktor 'nte+ral<

Pen"elesaian Persamaan 0i1erensial P0 &ksak

Pem%uktian Pan5an+ !aris Ba+i pada Se+iti+a

!rup dalam u%ik

Pen"elesaian Persamaan 0i1erensial P0 Tidak Domo+en Pen"elesaian Persamaan 0i1erensial P0 Domo+en

Pen"elesaian Persamaan 0i1erensial P0 Peu%a> Terpisa>

Mem%entuk Persamaan 0i1erensial

Persamaan 0i1erensial

Pem%a>asan Lati>an Soal 'nte+ral ;:< U9 SMA

Pem%uktian 'nte+ral cos 7 d7 sin 7

Persamaan !aris Sin++un+ Lin+karan den+an !radien Tertentu ;-<

Pro%lem ;-3< Kalkulus

Pem%uktian 'nte+ral sin d7 cos 7

'nte+ral aJ7 d7 Pro%lem ;-


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Pem%a>asan Lati>an Soal 'nte+ral ;< U9 SMA

Pem%a>asan Lati>an Soal 'nte+ral ;-< U9 SMA

Pem%a>asan Soal S'MAK U' 22C kode soal C-- ;<

Pem%a>asan Soal S'MAK U' 22C kode soal C-- ;-<

Pem%uktian umus Luas &lips

!aris Berat pada Se+iti+a

Pem%a>asan Lati>an Soal TPA 0eret ;)<

Mencari Solusi Persamaan Men++unakan Aturan ramer

Pem%a>asan Soal Persamaan dan Fun+si Kuadrat U9 SMA ;<

Koe1esien Binomial

Pem%uktian Lan+sun+

elasi Terurut Se%a+ian ;PGS&T<

Pem%a>asan Soal Lati>an &ksponen

Matematika "an+ Ane>

Bilan+an Prima dan 'rrasional

Pro%lem ;-)< Tri+onometri

Berapa cos -3 dera5at H

Pem%a>asan Lati>an Soal TPA 0eret ;8<

Penurunan umus tan;a %< dan tan ;a %<

Fi%onacci dan 'nduksi Matematika

0ari mana aJ a% %J H

Pro%lem ;-8< Men"elesaikan Ti+a Persamaan den+an GB&

Pro%lem ;-(<

Pro%lem ;-:< Tri+onometri

akin ( H

Akar : Bilan+an 'rrasional

sin -3 dera5at H

Pem%uktian umus Luas Selimut Kerucut

Pro%lem ;-< Tri+onometri

Pro%lem ;--<

Pem%uktian umus Tri+onometri cos;a %< dan cos;a %<

Pem%uktian Akar Bilan+an 'rrasional Secara !eometri

Soal Peluan+

Penurunan umus #arak Titik ke !aris

Pro%lem ;-2< Turunan dan Aritmatika

Bukti umus Tri+onometri sin;a %< dan sin;a %< Pem%a>asan Soal Lati>an &ksponen dan Lo+aritma U9 SMA ;:<

Pem%uktian umus *olume Bola

Pro"eksi *ektor

Pem%a>asan Lati>an Soal TPA 0eret ;8<

not>in+ is impossi%le on mat>ematic

Ke5adian Ane> pada 'nte+ral

!aris Tin++i pada Se+iti+a

Pro%lem ;C< Fun+si

Pem%uktian umus *olume Kerucut

Turunan lo+ 76 ln 76 aJ7 dan eJ7 H Pro%lem ;3< Fun+si

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Pem%uktian umus Luas Lin+karan

Turunan Fun+si Aturan Pan+kat

Kenapa 2R - H

Pem%uktian Aturan Kosinus

Dasil Kali Titik pada *ektor ;0ot Prdoduct<

'nvers Matriks

Kenapa ;-/aod<

Metode 9e$ton,ap>son ;9e$ton,ap>son Met>od<

Pem%uktian ( 8

Lo+aritma dan Si1at,Si1atn"a

Metode Ba+i,0ua ;Bisection Met>od<

Pem%uktian umus =Kecap? ;a%c< Mencari Akar Persamaan Kuadrat

Pem%a>asan Lati>an Soal Glimpiade Matematika ;<

Menentukan Suku ke,n pada Barisan Aritmatika Bertin+kat

Pro%lem ;)< 'nte+ral Tri+onometri

Pro%lem ;8< Tri+onometri Pem%uktian 'nte+ral cotJ 7 d7 ,cot 7 7

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Pem%uktian 'nte+ral tanJ 7 d7 tan 7 7

Pem%uktian 'nte+ral cosJ 7 d7 7 V sin 7

Pem%uktian 'nte+ral sinJ 7 d7 7 V sin 7

Pem%uktian 'nte+ral cot 7 d7 ln Wsin 7W

Pem%uktian 'nte+ral sec 7 tan 7 d7 sec 7

Pem%uktian 'nte+ral csc 7 d7 ln Wcsc 7 cot 7W

Pem%uktian tan 7 d7 ,ln Wcos 7W

Pem%uktian 'nte+ral cscJ 7 d7 ,cot 7

Pem%uktian 'nte+ral sec 7 d7 ln Wsec 7 tan 7W

Pem%uktian 'nte+ral csc 7 cot 7 d7 ,csc 7

'nte+ral Tri+onometri dan Pem%uktian

Fun+si Bi5ekti1 ;Satu,Satu dan Pada<

Fun+si Pada ;Sur5ekti1<

Fun+si Satu,Satu ;'n5ekti1<

Turunan Fun+si Aturan Pem%a+ian

Turunan Fun+si Aturan Perkalian

Pem%uktian umus Luas La"an+,La"an+

Pem%uktian umus Luas Bela> Ketupat

Luas Se+iti+a Tanpa 0iketa>ui Tin++i

Pem%uktian Formula Deron

Pem%uktian umus Luas Trapesium

Pem%uktian umus Luas Se+iti+a

Pem%uktian umus Luas Perse+i Pan5an+

Pem%a>asan Lati>an Soal TPA 0eret ;<

Pem%a>asan Lati>an Soal TPA Aritmatika ;<

Pro%lem ;(< 'nte+ral Tri+onometri

Pem%uktian 'nte+ral secJ 7 d7 tan 7 c

Pro%lem ;:< 'nte+ral Tri+onometri

Pro%lem ;< Al5a%ar

Pro%lem ;-< Al5a%ar

Pem%a>asan Lati>an Soal TPA 0eret ;-<

Pem%a>asan Lati>an Soal TPA Aritmatika ;-<

Asal Mula Bilan+an 'rrasional

Si1at Al5a%ar pada Bilan+an iil ;eal<

Pem%uktian den+an 'nduksi Matematika

U5i Ketelitian ;< Men+>itun+ Ban"ak Perse+i dalam Perse+i Kenapa - ;satu< Le%i> Besar 0ari 2 ;nolasan Lati>an Soal Glimpiade Matematika ;)<

Pem%a>asan Lati>an Soal Glimpiade Matematika ;8<

Pem%a>asan Lati>an Soal Glimpiade Matematika ;(<

Pem%a>asan Lati>an Soal Glimpiade Matematika ;:<

Pem%a>asan Lati>an Soal Glimpiade Matematika ;<

Pem%a>asan Lati>an Soal Glimpiade Matematika ;-<

Soal Glimpiade Matematika Ta>un 22C Pem%a>asan Soal Lati>an Tri+onometri U9 SMA ;(


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Pem%a>asan Soal Lati>an Tri+onometri U9 SMA ;:<

Pem%a>asan Soal Turunan U9 SMA ;:<

Pem%a>asan Soal Turunan U9 SMA ;<

Pem%a>asan Soal Turunan U9 SMA ;-<

Pem%a>asan Soal Lati>an S9MPT9 Matematika 0asar ;(<

Pem%a>asan Soal Tri+onometri U9 SMA ;<

Pem%a>asan Soal Tri+onometri U9 SMA ;-<

Men+>itun+ Kuadrat Bilan+an Ti+a 0i+it ;atusan< den+an Muda>

Pem%a>asan Soal Lati>an TPA Matematika

Pem%a>asan Soal Persamaan Linier U9 SMA

Pem%a>asan Soal Persamaan dan Fun+si Kuadrat U9 SMA

Pem%a>asan Soal Peluan+ U9 SMA

Pem%a>asan Soal Lati>an S9MPT9 Matematika 0asar ;:<

Pem%a>asan Soal Lati>an S9MPT9 Matematika 0asar ;<

Pem%a>asan Aritmatika TPA S9MPT9 2- ;Kode Soal --:<

Pem%a>asan TPA S9MPT9 2- ;Kode Soal --:<

Pem%a>asan Soal Lo+aritma dan &ksponen U9 SMA ;<

Pem%a>asan Soal Lo+aritma dan &ksponen U9 SMA ;-<

Pem%a>asan Soal Barisan dan 0eret !eometri U9 SMA

Pem%a>asan Soal Barisan dan 0eret Aritmatika U9 SMA

Pem%a>asan Soal Fun+si U9 SMA

Pem%a>asan Soal SPMB/S9MPT9 Lo+aritma dan &ksponen ;<

Pem%a>asan Soal SPMB/S9MPT9 Lo+aritma dan &ksponen ;-<

Pem%a>asan Soal Turunan SPMB/S9MPT9

Pem%a>asan Soal 0eret dan Barisan SPMB/S9MPT9

Pem%a>asan Lati>an Soal S9MPT9 Matematika 0asar ;-<

Pem%a>asan Soal Matematika 0asar S9MPT9 ;Kode Soal -3:<

Pem%a>asan Soal Matematika Sarin+an Masuk 'A'9 2- ;Kode Soal 2<

Pem%a>asan Soal Matematika Sarin+an Masuk 'A'9 2- ;Kode Soal -2<

Pem%a>asan TPA Komparasi Sarin+an Masuk 'A'9 2- ;Kode Soal 2-<

Pem%a>asan TPA Komparasi Sarin+an Masuk 'A'9 2- ;Kode Soal -2-<

Pem%a>asan TPA Aritmatika Sarin+an Masuk 'A'9 2- ;Kode Soal 2-<

Pem%a>asan TPA Aritmatika Sarin+an Masuk 'A'9 2- ;Kode Soal -2-<

Turunan Fun+si Aturan Selisi>

Turunan Fun+si Aturan Pen5umla>an

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