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Question
Find x, y satisfying the matrix equations
`[[X-Y 2 -2],[4 x 6]]+[[3 -2 2],[1 0 -1]]=[[ 6 0 0],[ 5 2x+y 5]]`
Solution
Given:
`[[X-Y 2-2],[4 x 6]]+[[3 -2 2],[1 0 -1]]=[[6 0 0],[5 2x+y 5]]`
`⇒[[x-y+3 2-2 -2+2 ],[4+1 x+0 6-1]] `= `[[6 0 0],[5 2x+y 5]]`
`⇒[[x-y+3 0 0 ],[5 x 5]]= [[6 0 0],[ 5 2x+y 5]]`
⇒x−y+3=6
⇒x−y=6−3
⇒x−y=3 ...(1)
Also,
x=2x+y
⇒−x=y ...(2)
Putting the value of y in eq. (1), we get
x−(−x)=3
⇒2x=3
`⇒ x = 3/2`
Putting the value of x in eq. (2), we get
`-(2/3)=y`
`⇒ y = -2/3`
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