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Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
1
Exercise 3.4
Using elementary transformation, find the inverse of each of the
matrices, if it exists.
Ques. 1:
A = [
]
We know, A = IA
[
] [
]
⇒[
] [
] (R2 ⟶ R2 – 2R1)
⇒[
] [
] (R2 ⟶
)
⇒[
] [
] (R1 ⟶ R1 + R2)
∴ = [
]
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
2
Ques. 2:
A = [
]
We know, A = IA
[
] [
]
[
] [
] (R1 ⟶ R1 – R2)
[
] [
] (R2 ⟶ R2 – R1)
∴ = [
]
Ques. 3:
A = [
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
3
Ques. 4:
A = [
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
4
Ques. 5:
A = [
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
5
Ques. 6:
A = [
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
6
Ques. 7:
A = [
]
We know, A = AI (Because A is an Square matrix)
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
7
Ques. 8:
A = [
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
8
Ques. 9:
A = [
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
9
Ques. 10:
A = [
]
We know, A = AI
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
10
Ques. 11:
A = [
]
We know, A = AI
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
11
Ques. 12:
A = [
]
We know, A = IA
Now, in the above equation, we can see all the Zeros in the
Second row of the matrix on the L.H.S.
Therefore, does not exist.
Ques. 13:
A = [
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
12
Ques. 14:
A = [
]
We know, A = IA
[
] [
]
⇒[
] [
] (R1 ⟶
)
⇒[
] [
] (R2 ⟶ R2 – 4R1)
Now, in the above equation, we can see all the Zeros in the Second
row of the matrix on the L.H.S.
Therefore, does not exist.
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
13
Ques. 15:
[
]
We know, A = IA
[
] [
]
(R1 ⟶ −R1 + R3)
[
] [
]
(R2 ⟶ R2 − 2R1)
(R3 ⟶ R3 − 3R1)
[
] [
]
(R2 ⟶ R2 −
)
[
] [
]
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
14
(R1 ⟶ R1 – R2)
(R3 ⟶ R3 + 5R2)
[
]
[
]
(R3 ⟶
)
[
]
[
]
(R1 ⟶ R1 + 5R3)
(R2 ⟶ R2 − 4R3)
[
]
[
]
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
15
[
]
Ques. 16:
[
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
16
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
17
Ques. 17:
[
]
We know, A = IA
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
18
Chapter - 3 Ex – 3.4 Matrices
PCM ENCYCLOPEDIA (www.facebook.com/pcmpedia)
19
