## Math 51, Winter 2013

In Winter 2013 I was a teaching assistant for Math 51.Our 11:00 section

Our 2:15 section

### Notes

I will post some notes on this page over the course of the quarter.- Notes on column space conditions, January 22.
- Notes on rank, nullity, existence, and uniqueness, January 27.
- List of some important definitions and propositions for midterm 1, January 27.
- Midterm 1 review session problems, January 30.
- Notes on diagonalizable matrices, February 12.
- Midterm 2 review session problems, February 26.
- List of some important definitions and propositions for midterm 2, February 26.
- Notes on tangent planes to surfaces, March 5.
- Lagrange multipliers example, March 12.
- Final review session problems, March 16.

### Practice Problems

The table below contains a good source of practice problems from old Math 51 exams. The first column contains a link to Midterm 1 from a previous quarter, and the second column contains the solution set (some exams have only a solution set). Each remaining column represents a section in Levandosky's Linear Algebra book. Each entry in the table is an exam problem that has been sorted into its appropriate section. For example, if you are interested in doing problems from section 4, then try problems 1(d), 6(a), 7(b), 9, or 10(c) from the first midterm in Winter 2012. I have left off some problems that require the cross product (but not others that can be solved without the cross product as in Example 4.3 in the book).

Section number from Levandosky's Linear Algebra book | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Exam | Sol | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

S12 | 3(b,c) | 7(c,d) | 1(a), 3(a) | 5(a) | 2(a) | 5(b) | 7(e,f) | 1(b), 4 | 2(b), 7(a,b) | 1(c), 6 | 7(g,h,i,j) | ||||||

W12 | W12 | 1(c) | 7(a) | 1(d), 6(a), 7(b), 9, 10(c) | 1(a,b,e), 5(a) | 4 | 3, 5(b) | 6(b), 10(a,b,d,e) | 8 | 2 | |||||||

F11 | F11 | 2 | 7 | 4(a) | 4(b), 5(b,d,f,g) | 5(a,c,e,h) | 6(a) | 1, 3, 11(i,j), 6(b), 9 | 4(c), 8 | ||||||||

S11 | S11 | 2(a) | 1(b,c) | 2(b,c) | 3 | 1(a) | 4 | 5, 6 | 7(a) | 7(b) | 7(c) | ||||||

W11 | W11 | 7(a), 9(a) | 1(a), 10(c) | 7(b), 9(b) | 2 | 4 | 1(d), 10(a) | 1(c,e), 3, 5 | 6 | 1(b), 8(a) | 8(b), 10(b) | ||||||

F10 | F10 | 1, 3(e) | 5 | 2 | 4, 9 | 3(a-d) | 8 |

For more problems through section 15, see this practice final with solutions and this final exam with solutions from the SSEA Math Module, Summer 2012. These cover the material from Math 51 Midterm 1.