Engineering-Mathematics

Question 15

Find the inverse of the matrix

A
B
C
D

Engineering-MathematicsLinear-AlgebraGATE 1994

Question 15 Explanation:

Using eigen values, the characteristic equation we get is,
-λ³ + 2λ² – 2 = 0
Using Cayley-Hamiltonian theorem
-A³ + 2A² – 2I = 0
So, A^-1 = 1/2 (2A – A²)
Solving we get,

Correct Answer: B

Question 15 Explanation:

Using eigen values, the characteristic equation we get is,
-λ³ + 2λ² – 2 = 0
Using Cayley-Hamiltonian theorem
-A³ + 2A² – 2I = 0
So, A^-1 = 1/2 (2A – A²)
Solving we get,