If A = , find
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)
⇒ 16 + x = 24
⇒ 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
⇒ A2.A-1 + 8I.A-1 = 8AA-1
⇒ A.(AA-1) + 8A-1 = 8I [AA-1 = I]
⇒ A(I) + 8A-1 = 8I
⇒ A + 8A-1 = 8I
⇒ 8A-1 = – A + 8I
Ans.