Math 115A: Linear Algebra

Date  Topic  Homework 
10/2 (Fri) 
Sets and functions 
Prove that the complex numbers
satisfy the axioms of a field. 
10/5 (Mon)  Section 1.2: Vector spaces  Please
note that I use the problem numbering from Friedberg,
4th Edition. Section 1.2: 1,4,8,9,10,11,13,16,20 In Problems 13 and 16, if V is a vector space, then verify all the axioms of a vector space. 
10/6 (Tues) 
Quiz 1 
Go to Gradescope to take the quiz between 12:01 am and 11:59 pm Pacific Time on Tues 10/6. The only things you're allowed to use are: the Friedberg textbook, the class notes/videos, and your completed HW. You may not discuss the test with anyone and you may not give or solicit help. Besides the class materials on CCLE, the internet is off limits. Today's a test run, so you're allowed 2 hours from the time you start the quiz. Important: Please handwrite your solutions!!! 
10/7 (Wed)  Section 1.3: Subspaces  Section 1.3: 1,6,8,11,15,20,23,24,30 
10/9 (Fri)  Section 1.4: Linear combinations  Section 1.4: 1,2(a)(c)(e),3(a)(c)(e),7,8,13,14 
10/12 
Section 1.5: Linear dependence/independence  Section 1.5: 1,2(a)(c)(e),4,5,9,15,18 
10/13 (Tues) 
Quiz 2 
Go to Gradescope to take the quiz between 12:01 am and 11:59 pm Pacific Time. You're allowed 50 minutes from the time you start the quiz  about 30 minutes to do the quiz and another 20 minutes to upload your solutions. Important: Please handwrite your solutions!!! 
10/14 
Section 1.6: Bases and dimension  Section 1.6: 2(a)(c)(e),3(a),6,14,15,17 (We may not get to the definition of dimension until next week; simply take it to be the number of elements of the basis you constructed.) 
10/16 
Section 1.6: Bases and dimension  Section 1.6: 12,20,24,26,28,33,34 
10/19 
Section 2.1: Linear transformations  Section 2.1: 7,8,9,14(b),15 
10/20 (Tues) 
Quiz 3 

10/21 
Section 2.1: Linear transformations  Section 2.1: 1,2,5,6,17,24,26,28 
10/23 
Section 2.2: Matrix representation of a linear transformation  Section 2.1: 11,13 Section 2.2: 1,2(a)(c)(f),3,4 
10/26 
Section 2.2: More on matrix
representations Section 2.3: Composition of linear transformations 
Section 2.2: 5,8,10,11 Section 2.3: 2,3 
10/27 (Tues) 
Quiz 4 

10/28 
Section 2.3: More on compositions of linear transformations  Section 2.3: 1,4,12,17 
10/30 
Section 2.4: Invertibility and isomorphisms  Section 2.4: 1, 2(a)(c)(e),3,7,14,15,16,17 
11/2 
Section 2.5: Change of coordinates  Section 2.5: 1,2(a)(c),3(a)(c),5,7,10,13 
11/3 (Tues) 
No quiz this week 

11/4 
Midterm Exam  Midterm
Info Sample Problems 
11/6 
Quotient spaces  1. Complete the proof that the
quotient space V/W is a vector space. Namely, verify
the axioms (VS1)(VS8) that were not verified in class. 2. Complete the proof that if f: V>W is a linear map, then V/Ker f is isomorphic to Im f. 
11/9 
Section 4.4: Review of determinants  Section 4.4: 1,2,3(a)(c)(g),4(a),5,6 
11/10 (Tues) 
Quiz 5 

11/11 
University Holiday
(Veterans Day) 

11/13 
Section 5.1: Eigenvalues and
eigenvectors 
Section 5.1:
3(a)(b)(c)(d),4(a)(b)(e) 
11/16 
Factoring
polynomials 
Section
5.1: 7,8,14,15(a),16(a),17,22,23 
11/17 (Tues) 
Quiz 6 

11/18 
Section 5.2: Diagonalizability  Section 5.2:
1(a)(g),3(a)(d)(e),8 
11/20 
Section 5.2: Some applications 
Section 5.2: 9(a),10,11,12,19 
11/23 
Section 5.2: Direct sum
decompositions 
Section 5.2:
1(h)(i),14,15,20,22 
11/24 (Tues) 
Quiz 7 

11/25 
Section 6.1: Inner products 
Section 6.1: 1,2,3,4,6,8,9 
11/27 
No Class (Thanksgiving) 

11/30 
Section 6.1: Inner products Section 6.2: GramSchmidt orthogonalization 
Section 6.1: 12,16,17,23 Section 6.2: 1(a)(b)(f)(g),2(b)(c)(g)(i) 
12/1 (Tues) 
Quiz 8 

12/2 
Section 6.2: GramSchmidt
orthogonalization 
Section 6.2:
4,5,6,7,9,13,19(c),21 
12/4 
Section 6.3: Adjoints 
Section 6.3:
1,2(a)(c),3(a)(c),4,14 
12/7 
Section 6.4: Selfadjoint and
normal operators 
Section 6.4: 1,2(a)(c)(d),4,5,9,12,16,20 (Note that we'll discuss normal operators next time) 
12/8 (Tues) 
Quiz 9 

12/9 
Section 6.4: Selfadjoint and
normal operators 
Start doing sample problems
for final exam 
12/11 
Review/summary (we'll do some
sample problems) 

12/15 (Tues)  Final
Exam 
Final
Info Sample Problems 