Solve the following equations for X and Y :
`2X-Y=[(3,-3,0),(3,3,2)], 2Y+X=[(4,1,5),(-1,4,-4)]`

Answer

`X=[(2,-1,1),(1,2,0)], Y=[(1,1,2),(-1,1,-2)]`

Explanation

Given,
`2X-Y=[(3,-3,0),(3,3,2)]`
Multiplying both sides by 2, we have
`4X-2Y=2 [(3,-3,0),(3,3,2)]`
`4X-2Y=[(6,-6,0),(6,6,4)]` (1)
Also given,
`X+2Y=[(4,1,5),(-1,4,-4)]` (2)
Adding (1) and (2), we have
`5X=[(6,-6,0),(6,6,4)]+[(4,1,5),(-1,4,-4)]`
`=[(6+4,-6+1,0+5),(6-1,6+4,4-4)]`
`=[(10,-5,5),(5,10,0)]`
`:. X=1/5 [(10,-5,5),(5,10,0)]=[(2,-1,1),(1,2,0)]`
Putting the value of X in (2), we have
`[(2,-1,1),(1,2,0)]+2Y=[(4,1,5),(-1,4,-4)]`
or `2Y=[(4,1,5),(-1,4,-4)]-[(2,-1,1),(1,2,0)]`
`=[(4-2,1+1,5-1),(-1-1,4-2,-4-0)]`
`=[(2,2,4),(-2,2,-4)]`
`:. Y=[(1,1,2),(-1,1,-2)]`
Hence,
`X=[(2,-1,1),(1,2,0)]` and `Y=[(1,1,2),(-1,1,-2)]`