Q. 344.5( 6 Votes )

# If A = <img

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 β¦(i)

y = 8 β¦(ii)

56 = 7y β¦(iii)

32 + x = 5y β¦(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 = β A + 8I

Ans. π³ = 8, π΄ =8 and A-1 = . .

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