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Question
If A = `[[3,1] , [7,5]]`, find the values of x and y such that A2 + xI2 = yA.
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Solution
Given that: A = `[[3,1] , [7,5]]`
Now, A2 = A.A = `[[3,1] , [7,5]] [[3,1] , [7,5]]`
= `[[9 +7, 3+5], [ 21 + 35, 7 + 25]]`
= `[[16,8], [56,32]]`
∴ A2 + xI2 = yA
`[[16,8], [56,32]] + x [[ 1,0], [0,1]] = y [[3,1] ,[7,5]]`
`[[16 +x ,8],[ 56 , 32+x]] = [[3y, y],[7y,5y]]`
Comparing the corresponding entries of equal matrices, we have ⇒ y = 8
and 16 + x = 3y
∴ x = 3 x 8 - 16
= 24 - 16
= 8
Hence, the required values of x is 8 and y is 8.
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