1.

Find X and Y, if `X+Y=[[5, 2],[ 0, 9]]`and `X-Y=[[3 ,6],[ 0,-1]]`.

Answer» Adding the given matrices, we get
`(X+Y)+(X-Y)=[{:(5,2),(0,9):}]+[{:(3," "6),(0,-1):}]`
`implies" "2X=[{:(5+3,2+6),(0+0,9+(-1)):}]`
`implies" "2X=[{:(8,8),(0,8):}]impliesX=(1)/(2).[{:(8,8),(0,8):}]=[{:(4,4),(0,4):}].`
On subtracting the given matrices, we get
`(X+Y)-(X-Y)=[{:(5,2),(0,9):}]-[{:(3,6),(0,-1):}]`
`implies" "2Y=[{:(5-3,2-6),(0-0,9-(-1)):}]=[{:(2,-4),(0,10):}]`
`implies" "Y=(1)/(2)[{:(2,-4),(0,10):}]=[{:(1,-2),(0," "5):}].`
Hence, `X=[{:(4,4),(0,4):}]" and "Y=[{:(1,-2),(0,5):}].`


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