3 10/12

1. New: 7.3.10. Old: 6.3.10. Find $\Omega$ by augmenting $A$ by the three by three unit matrix. Use the procedures given in class (i.e. first reduce A to echelon form, and then reduce it farther to row reduced/row canonical form. Verify that indeed $\Omega A=A_R$.

2. New: 7.4.12 Old: 6.4.12 Bases must be cleaned up as much as possible.

3. New: 7.5.6, 7.6.6, 7.6.13, 7.6.14 Old: 6.5.6, 6.6.6, 6.6.21, 6.6.22. Write the general solution of the first problem as a linear combination of basis vectors (as column vectors).

4. New: 7.7.8, 7.7.14 Old: 6.7.8, 6.7.14. Write the general solution as a linear combination of basis vectors (as column vectors) plus a constant vector. Do not reduce to reduced echelon form; reduce to echelon form only and solve it from there.

5. New: 7.8.6 Old: 6.9.6 Use elimination to find the inverse.

6. New: 8.5.6 Old: 7.5.6 Do NOT use row or column operations!

7. New: 8.5.6 Old: 7.5.6 Use row operations ONLY to reduce to upper triangular form!

8. New: 8.7.8 Old: 7.7.8. Use minors to do so.