MSM 711

Hand-in assignment #2

Due Tuesday, November 4 at the beginning of class

For any matrix computations of sums, differences, products or transposes please show all steps. Also, for computing inverses of 2x2 matrices please use Theorem 3.2.7 on p. 99 and show your work. You may use your calculator for finding inverses of any matrix larger than a 2x2 (just make sure you say that’s what you used.) Of course, you may use the calculator to check any of your answers.

Use the following matrix definitions for problems 1 – 10.

Let , , and

Find each of the following, or else explain (in complete sentences!) why it does not exist.

1. B + D

2. B + C

3. CA

4. AB

5. BC – 4C

6.

7.

8.

9.

10.

11. Let . Find a 2 x 3 matrix N with distinct entries (i.e. all entries must be different) so that MN = .

12. Given the system of equations:

a. Express the system in the form Ax = b by writing down the coefficient matrix A and constant vector b.

b. Find if it exists. If it does not, state how you know.

c. Does the system have a solution or solutions? If so, find it (or them) by any method. If not explain why not.