   Chapter 11.2, Problem 34E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS 23-36 ■ Matrix Operations The matrices A , B , C , D , E , F , G and H are defined as follows. A = [ 2 − 5 0 7 ] B = [ 3 1 2 5 1 − 1 3 ] C = [ 2 − 5 2 0 0 2 − 3 ] D = [ 7 3 ] E = [ 1 2 0 ] F = [ 1 0 0 0 1 0 0 0 1 ] G = [ 5 − 3 10 6 1 0 − 5 2 2 ] H = [ 3 1 2 − 1 ] Carry out the indicated algebraic operation, or explain why it cannot be performed. (a) ( D A ) B (b) D ( A B )

To determine

(a)

To find:

The result of the matrix operation (DA)B and the reason if it does not exist.

Explanation

Given:

The matrices A, B, C, D, E, F, G and H are defined as follows.

 A=[2−507] B=[31251−13] C=[2−52002−3] D= E= F= G=[5−310610−522] H=[312−1]

Approach:

Two matrices A and B can be multiplied if and only if the number of columns in A is same as the number of rows in B.

If A=[aij] is an m×n matrix and B=[bij] an n×k matrix, then their product is the m×k matrix C=[cij], where cij is the inner product of the ith row of A and the jth column of B.

Calculation:

Consider the matrix operation (DA)B and the given matrices A=, B= and D=

To determine

(b)

To find:

The result of the matrix operation D(AB) and the reason if it does not exist.

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