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Math 115A, Lecture 5, Fall 2010

Homework 1 — Assigned 9/24, due 10/1:

From the “supplement” at the end of the book (p. 624): 3, 4, 9, 21, 24, 26
Sec. 1.2: 7, 8, 11, 14, 15, 19, 21
(For those of you who don't have the UCLA special edition of the textbook, here are the exercises from p. 624.)

Homework 2 — Assigned 10/1, due 10/8:

Handout

Homework 3 — Assigned 10/8, due 10/15:

Handout

Homework 4 — Assigned 10/15, due 10/22:

Sec. 2.1: 7, 9, 10, 12, 13, 15, 16, 18, 19, 20, 24, 25

Homework 5 — Assigned 10/22, due 10/29:

Handout (Note: The problems originally assigned from Section 2.2 have been taken off this assignment. They will be reassigned as part of next week's homework.)

Homework 6 — Assigned 10/29, due 11/5:

Sec. 2.2: 2(a,c,e,g), 5(d,f,g), 11, 12, 16
Sec. 2.3: 3, 9, 11, 12, 13
Sec. 2.4: 2(a,b,c,d), 3(a,b,c), 4, 6, 16, 17, 20

Hint for 2.2, #12: Refer to problem 33 from Section 1.6. (This was part of homework 3.)

Hint for 2.2, #16: Start with a basis {u₁, ... , u_n} for N(T) (where n = nullity(T)), and extend this to a basis {u₁, ... , u_n, v₁, ... , v_r} for V (where r = rank(T)). Show that {T(v₁), ... , T(v_r)} is linearly independent, and extend this to a basis for W. Be careful to order the two bases appropriately in order to make the resulting matrix diagonal. (Note that most of this hint follows the proof of the Dimension Theorem exactly.)

Homework 7 — Assigned 11/5, due 11/12:

Handout

Homework 8 — Assigned 11/12, due 11/19:

Handout

Homework 9 — Assigned 11/19, due 11/29:

Sec. 5.2: 1(a-g), 2, 3(b,c,d), 8, 18, 19

Homework 10 — Assigned 11/29, due 12/8 (at or before the review session):

Sec. 6.1: 3, 9, 10, 11, 12, 15(a), 17, 20

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