PLEASE HELP ME SOLVE

Question

given the matrices R,S AND T find 2RS - 3ST.
R = 1 0 2          S= 0 -1 2             T= -2 3  0

       2 1 5               3  1  0                 -3  2  2

       2 3 1               4  2  1                   -1 1  0

Answer 1

Malissa,

 

Let's find RS, then ST and then multiply both matrices accordingly. Then subtract.

 

I'll do a few calculations here and then give you the full matrix.

The top left most entry for RS is the product of first row of R and first column of S as follows:

[1 0 2] x [0 3 4] = 1*0+0*3+2*4 = 8

 

The top middle entry is the product of the first row of R and the second column of S:

[1 0 2] x [-1 1 2]=1*-1+0*1+2*2=3

 

Basically RS=

8 3 4

23 9 9

13 3 5

 

ST=

1 0 -2

-9 11 2

-15 17 4

2RS=

16 6 8

46 18 18

26 6 10

 

3ST=

3 0 -6

-27 33 6

-45 51 12

 

Then 2RS-3ST=

13 6 14

73 -15 12

71 -45 -2

 

Hope that helps!