1. Find the transposed matrix which maps the basis
of
to the basis
.
2. Show that the transposed matrix which maps the basis
to the basis
of
is regular .
3. Find all eigenvalues and all eigenvetors of the following matrices.
4. Find the eigenvalue of the square matrix which satisfies
5. Let the eigenvalues of be
. Then show that the eigenvalues of
are
.
6. Given
. Find
using Cayley-Hamilton theorem.
7. Suppose is the matrix of order 2. Find all
satisfying
.