Answer to Question #42307 in Linear Algebra for anuirodh

Question

Let
A =5 4 −4
6 7 −6
12 12 −11

a) Find the adjoint of A. Find the inverse of A from the adjoint of A.
b) Find the characteristic and minimal polynomials of A. Hence find its eigenvalues and eigenvectors.
c) Why is A diagonalisable? Find a matrix P such that P^(−1) AP is diagonal.
d) Verify Cayley-Hamilton theorem for A. Hence, find the inverse of A.