Question #46091

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

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

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