# Math 309 Fall 2019 Section 4 course homepage

The classes are on Mondays and Wednesdays at A334 Wells Hall, 4:10 -- 5:30pm. Check out MSU Academic Calendar for holidays, etc. First class is on Wednesday, August 28.

Lecturer: Ilya Kachkovskiy, ikachkov@msu.edu

Office: Wells Hall C300, office hours: Monday 2:30-3:30, Wednesday 11-12. Email for more office hours or to make an extra appointment.

Homework 1, due Wednesday, September 11:

Section 1.1, exercises 1d, 2, 3d, 6f, 9.

Section 1.2, exercises 1, 2 (for exercises 1 and 2, just list the yes/no answers), 3de, 5b, 6b, 10, 13, 15 (read example from the book first if not covered in class).

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Homework 2, due Wednesday, September 19:

Section 1.3: 1ef, 2abf, 3abf, 8b (compute left and right hand side and check if they are the same), 15.

Section 1.4: 1b, 4, 7, 12, 20 (use definition: multiply the right hand side by I-A and check), 21.

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Homework 3, due Wednesday, September 26:

Section 1.4: 34, 35, 36.

Section 1.5: 3ab (hint: find which row operation you need to perform on A to get B), 7ab (use the same scheme as in the proof in class), 10bef, 15 (hint: a_1,a_2,a_3 are columns of A in the book notation. Look at the equation 2a_1+a_2-4a_3=0. Can you guess a nontrivial solution to Ax=0? Remember than Ax can be expressed as a linear combination of columns).

Handout 1: pdf: complete all proofs. Some of them will be done in class.

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Homework 4, due Wednesday, October 9:

Section 1.4: 24, 25.

Section 1.5: 29, 30.

Section 3.2: 2 (explain), 3 (only answers), 4bc (do same way as in class or in Example 9), 5abc (explain), 11b, 12a, 13b, 15ab, 19ad, 23.

Try to prove as many lemmas as possible from Handout 1 from previous homework. Read lemmas pdf.

Axiom problems for homework: 1) Given 2v=3v, prove that v=0 using only axioms (no lemmas).

2) Prove (v+w)+(u+v)=2v+(w+u) using only axioms (no lemmas).

New problems for homework 4!!!!

Section 3.3: 2bc, 3bc, 6 (use definition), 13.
Section 3.4: 2bc, 3ab.

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Midterm exam 1 is on Wednesday, October 2nd, in class. Review sheet.
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Homework 5, due Wednesday, October 16:

3.4: 4, 5, 6, 9, 14.

3.5: 1, 4, 5, 9.

3.6: 1ab.

Homework 6, due Wednesday, October 23:

3.6: 3, 4def, 5def, 8, 9, 10, 13 (read "Linear systems revisited" part of Section 3.2), 18.

4.2: 2bc, 3bc, 7.

Homework 7, due Wednesday, October 30:

4.2: 14, 16, 18

4.3: 1, 2, 3, 4, 5abc, 7, 9

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Midterm exam 2 is on Wednesday, Nov 6, in class.
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Homework 8, due Wednesday, November 13:

2.1: 2, 3bcg, 4, 5, 6, 11.

2.2: 1bc, 2, 3ef, 4, 7, 9, 10 (not graded), 11 (not graded)

Homework 9, due Wednesday, November 20:

2.3: 1bc, 2bc, 6,

5.1: 3, 14, 17, 18.

5.2: 1bcd, 3, 4, 12.

Homework 10, due Wednesday, December 4:

5.3: 1bc, 2bc, 3b, 4b, 5a.

5.5: 1, 2, 3, 4, 5, 6, 7, 14, 15, 21 (read Theorem 5.5.6), 22.