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

A---B---C

G---H---I /////////////////////////// is Matrix A

M---N--O

D---E---F

J---K----L ///////////////////////// is Matrix B

R---S---T

Matrix AB is obtained by

AD+BJ+CR---------------AE+BK+CS-----------------AF+BL+CT

GD+HJ+IR----------------GE+HK+IS------------------GF+HL+IT

MD+NJ+OR--------------ME+NK+OS-----------------MF+NL+OT

The specific values for the elements of Matrices A & B given above yield Matrix AB as

(-13)----------------(-2)-------------------(-6)

(6)-------------------(7)---------------------(6)

(13)----------------(13)--------------------(12)

For c given as 2, c(AB) is then equal to Matrix AB with every element doubled:

(-26)----------------(-4)-----------------(-12)

(12)-----------------(14)-----------------(12)

(26)----------------(26)------------------(24)

Obtain (cA)B by multiplying every element in Matrix A by c (equal to 2)

and then by multiplying Matrix (cA) by Matrix B. The result will come to:

(-26)----------------(-4)-----------------(-12)

(12)-----------------(14)-----------------(12)

(26)----------------(26)------------------(24)

It can be seen that c(AB) and (cA)B give identical results and are thus equal.