We can define a matrix in either of the following forms:

> A = [4 0 5; -1 3 2] > A = [4 0 5 -1 3 2]You can execute basic matrix operations as follows.

> 5 * A > A + B > A * B

EXAMPLES 1. Let , , and .

- Compute .
- Is the matrix sum defined?
- Compute .
- Compute .

EXAMPLES 2. Compute in each of the following:

- and .
- and .

EXAMPLE 3 Let and . Show that these matrices do not commute.

Matlab/Octave can compute the power `A^k`
and the transpose `A'` of `A` as follows.

> A^5 > A'

EXAMPLE 4. Let and . Compute and .

EXAMPLE 5.
Write the function `rmatrix()` that will create an
matrix with random entries.
Then create a matrix with random entries between and .

Department of Mathematics