Use a graphing utility to perform the operations for the matrices A, B, and C, and the scalar c.

Question

A = -3 -2 3

0 2 -1

1 4 -2

B= 1 -1 0

2 4 3

-2 1 0

C = 3 -2 3

-4 0 -2

-1 1 3 c = 2

(a) c(AB)

_____ _____ _____

_____ _____ _____

_____ _____ _____

(b) (cA)B

_____ _____ _____

_____ _____ _____

_____ _____ _____

Write a brief statement comparing the results of parts (a) and (b).

The matrix c(AB) (is the same as) or (is different from)  the matrix (cA)B.

Answer 1

Using a graphing utility, you can find that the answer is the same for the first two parts. This question is asking about the associative property of matrix multiplication. If you consider the scalar c as a 1 x 1 dimensional matrix, then the same principle still applies. If we have three matrices A, B, and C (or c in this case), then the following relationship holds:

C(AB) = (CA)B.