1. For matrices
, evaluate the followings:
2. For matrices
, find
.
3. For the matrix
, calculate
.
4. Let and
be symmetric matrices of the order
. Show that
is a symmetric matrix.
5. Let and
be symmetric matrices of the order
. Find the necessary and sufficient conditions so that
is a symmetric matrix.
6. Suppose that is a skew symmetric matrix. Then show that
is a symmetric marix.
7. Find matrices so that the product of
is interchangeable.Here,
are different real numbers.
8. Show that any square matrix can be expressed by the sum of a symmetric matrix and a skew symmetric matrix.
9. Find the product of and
, where
.