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

Explanation

Given `2X-Y=[{:(3,-3,0),(3,3,2):}]`
on multiplying both sides by 2, we get
`4x-2y=2[{:(3,-3,0),(3,3,2):}], 4x-2y=[{:(6,-6,0),(6,6,4):}]`
also given `x+2y= [{:(4,4,4),(-1,4,-4):}]`
Adding Eqs. (i) and (ii) , we get
`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):}]rArr X=[{:(2,-1,1),(1,2,0):}]`
putting the value of X in Eq. (ii), we get
`[{:(2,-1,1),(1,2,0):}]+2Y=[{:(4,1,5),(-1,4,-4):}]`
`rArr 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,-2):}]`
`Y = [{:(1,1,2),(-1,1,-2):}]`
Hence, `X = [{:(2,-1,1),(1,2,0):}] and Y= [{:(2,-1,1),(-1,1,-2):}]`