Find X and Y, if(i) `X+Y=[7 0 2 5]`and `X-Y=[3 0 0 3]`(ii) `2X+3Y=[2 3 4 0]`and `3X+2Y=[2-2-1 5]`

Answer

N/a

Explanation

`(i) X+Y=[{:(7,0),(2,5):}].. .(1) `
`X-Y=[{:(3,0),(0,3):}].. .(2)`
on adding,` 2X=[{:(10,0),(2,8):}]implies X=[{:(5,0),(1,4):}]`
put the values of X in equation (1),
`[{:(5,0),(1,4):}]+y=[{:(7,0),(2,5):}]`
`implies Y=[{:(7,0),(2,5):}]-[{:(5,0),(1,4):}]=[{:(2,0),(1,1):}]`
(ii) `2X+3Y=[{:(2,3),(4,0):}].. .(1)`
`3X+2Y=[{:(2,-2)(-1,5):}] .. .(2)` Multiplying equation (1) by 3 and equation (2) by 2 and subtriacting,
`6X+0Y=[{:(6,9),(12,0):}]`
`6X+4Y =[{:(4,-4),(-2,10):}]`
`-" " -" "-`
`overline (5Y=[{:(2,13),(14,-10):}])`
`implies Y=[{:((2)/(5),(13)/(5)),((14)/(5),-2):}]`
multiplying equation (2) by 3 and equation (1) 2 and subtracting,
`9X+6Y=[{:(6,-6),(-3,15):}]`
`4X+6Y=[{:(4,6),(8,0):}]`
`-" " -" " -`
`overline(5X=[{:(2,-12),(-11,15):}])`
`implies X=[{:((2)/(5),-(12)/(5)),(-(11)/(5),3):}]`