Question

If `A=((3,2), (-3,-4))` and `B=((0,-5),(-2,1))`, What are the matrices X and Y such that 2A -3X = B and 3A+2Y = 2B?

Answer 1

`X=((2,3),(-4/3,-3))` and `Y=((-9/2,-8),(5/2,7))`

Explanation:

As `2A-3X=B`, `3X=2A-B` and

`X=1/3(2A-B)`

= `1/3[2((3,2),(-3,-4))-((0,-5),(-2,1))]`

= `1/3((2xx3-0,2xx2-(-5)),(2xx(-3)-(-2),2xx(-4)-1))`

= `1/3((6,9),(-4,-9))`

= `((2,3),(-4/3,-3))`

and as `3A+2Y=2B`, `2Y=2B-3A`

and `Y=1/2(2B-3A)`

= `1/2[2((0,-5),(-2,1))-3((3,2),(-3,-4))]`

= `1/2((2xx0-3xx3,2xx(-5)-3xx2),(2xx(-2)-3xx(-3),2xx1-3xx(-4)))`

= `1/2((-9,-16),(5,14))`

= `((-9/2,-8),(5/2,7))`