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?

1 Answer
Jan 18, 2018

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))