# Answer to Question #42307 in Linear Algebra for anuirodh

Question #42307

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.

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.

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