If `X` and `Y` are `2xx2` matrices, then solve the following matrix equations for `X` and `Ydot` `2X+3Y=[2 3 4 0]` , `3X+2Y=[-2 2 1-5]`

Explanation

We have, ` 2X+3Y=[{:(2,3),(4,0):}]`
and `3X+2Y=[{:(-2,2),(1,-5):}]`
On subtracting Eq. i from Eq. ii we get
`therefore (3X+2Y)-(2X_3Y)=[{:(-2,-2,2-3),(1-4,-5,0):}]`
`(X-Y)=[{:(-4,-1),(-3,-5):}]`
On adding Eqs. I and ii, we get
`( 5X+5Y)=[{:(0,5),(5,-5):}]`
`rArr (X+Y)=(1)/(5)[{:(-2,0),(-2,-6):}]`
`therefore X=[{:(-2,0),(-1 ,-3):}]`
From Eq. iv,
`[{:(-2,0),(-1,-3):}]+y=[{:(0,1),(1,-1):}]`
`therefore Y=[{:(2,1),(2,2):}]` and ` X=[{:(-2,0),(-1, -3):}]`