   Chapter 2.5, Problem 28E

Chapter
Section
Textbook Problem

Let A = [ 0 3 0 1 0 1 0 2 0 ] B = [ 2 4 5 3 − 1 − 6 4 3 4 ] C = [ 4 5 6 3 − 1 − 6 2 2 3 ] a. Compute A B .b. Compute A C .c. Using the result of parts (a) and (b), conclude that A B = A C does not imply that B = C .

To determine

a)

To compute:

Product AB for the given matrices.

Explanation

Given:

The given matrices are:

A=, B= and C=

Calculation:

Consider the matrix A and matrix B,

A= and B=

Compute the product AB for considered matrices as follows,

AB==[0×2+3×3+0×40×4+(3×1)+0×3

To determine

b)

To compute:

Product AC for the given matrices.

To determine

c)

To conclude:

That product AB=AC does not imply that B=C.

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