EE107

Mathematical Methods for

Engineers I

Lecture 1: Matrices

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Properties for matrix multiplication

If r represent scalar elements and A, B and C represent

matrices:

A(BC) = (AB)C

A(B+C) = AB+AC (distributive properties )

(B+C)A = BA +CA (distributive properties )

r(AB) = (rA)B = A(rB)

I.A = A = A.I (I is identity matrix)

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Caution:

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Example:

To illustrate, consider the following 3 by 3 matrix,

To compute the minor M23 and the cofactor C23, we find the

determinant of the above matrix with row 2 and column 3 removed

.

So the cofactor of the (2,3) entry is

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EXERCISE:

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Adj(A)=Adjoint(A)

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Example:

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Example:

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Summary

In this Lecture, we learned:

Scalar multiplication, addition,

subtraction, multiplication of matrices

Minor, Cofactor and Determinants of

Matrix

Adjoint and Inverse of Matrix

Some special matrices