Answer to Question #46091 in Engineering for Sapna

Question

Let
A =
2
4
5 4 4
6 7 6
12 12 11
3
5
a) Find the adjoint of A. Find the inverse of A from the adjoint of A. (4)
b) Find the characteristic and minimal polynomials of A. Hence find its eigenvalues and
eigenvectors. (6)
c) Why is A diagonalisable? Find a matrix P such that P
1
AP is diagonal. (2)
d) Verify Cayley-Hamilton theorem for A. Hence, find the inverse of A