Answer :

Given:

To find: value of x and y


Given equation: A2 + xI = yA


Firstly, we find the A2





Putting the values in given equation


A2 + xI = yA






On Comparing, we get


16 + x = 3y …(i)


y = 8 …(ii)


56 = 7y …(iii)


32 + x = 5y …(iv)


Putting the value of y = 8 in eq. (i), we get


16 + x = 3(8)


β‡’ 16 + x = 24


β‡’ x = 8


Hence, the value of x = 8 and y = 8


So, the given equation become A2 + 8I = 8A


Now, we have to find A-1


Finding A-1 using given equation


A2 + 8I = 8A


Post multiplying by A-1 both sides, we get


(A2 + 8I)A-1 = 8AA-1


β‡’ A2.A-1 + 8I.A-1 = 8AA-1


β‡’ A.(AA-1) + 8A-1 = 8I [AA-1 = I]


β‡’ A(I) + 8A-1 = 8I


β‡’ A + 8A-1 = 8I


β‡’ 8A-1 = – A + 8I







Ans. 𝒳 = 8, 𝒴 =8 and A-1 = . .


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