# Math 22: Lecture schedule and practice problems - FALL 2016

Note: X-hour dates are shown for Section 1 (Barnett); Section 2 (Tanabe) has the X-hr on Thursday not Tuesday.

weekdatereading daily topicsworksheets, links, demospractice problems from book
1Sep 12 M website, 1.1 Systems of linear equations.solnsets5,7,9,11,13,21,27.
13 Tu X-hrResources on proofsdoing proofs. proofs
14 W 1.2Row reduction, echelon forms (slides, more)echform3,5,13,15,19,21(ans:ffttf),31.
16 F 1.3Vector equations (lin combos, span)span7,9,11(ans is wrong!),15,21,22, 23(ans:ffttf)
219 M 1.4-1.5The matrix equation Ax=b, solution sets.matvec1.4: 3,9,15,19,23(ans:ftfttt); 1.5: 7,15,23(ans:tffft),27,31.
20 Tu X-hrResources on proofsmore critical thinking about proofs. proofsrecap, proofs2
21 W 1.6 (last 2 pp), 1.7 HW1 due. App: network flow. Linear independence.paramsoln1.6: 12(ans:80),13; 1.7: 5,13,17,21(ans:fftt),25,27,33,37,39.
23 F1.8Intro to linear transformations linxform1.8: 7,9,11,13,17,19,21(ans:tffft),27.
326 M1.9 The matrix of a linear transformation.onto1.9: 3,9,15,17,23(ans:ttfff),25,35.
27 Tu X-hr1.10 (last 2 pp), 2.1extra lecture. App: difference eqns. Matrix operations.matmat 1.10: 9. 2.1: 3,5,9,15(ans:ffttf),16(ans:tftft),17,21,23.
28 W2.2HW2 due. The inverse of a matrix.inverse2.2: 7,10(ans:ftftt),13,17,19,21,31,35.
30 F2.3Characteristics of invertible matrices. prove stuff on p.112 2.3: 3,7,11(ans:ttftt),15,17,22,27,33.
4Oct 3 M3.1-3.2Determinants and their properties. detred 3.1: 5,9,11,35,37; 3.2: 7,23,27(ans:tttf),29,31,33.
4 Tu X-hr Resourceslinear algebra on the computer, MATLABcode
5 W4.1HW3 due. Vector spaces and subspaces (not this!) subspace4.1: 2,3,7,9,15,17,31; go over mini quiz 1.
7 F4.2Null and column spaces. 4.2: 3, 7, 11, 17, 21, 23, 25(ans:tftftt). [For some harder ones: 31, 35]
510 M4.3Bases, spanning set theorem. basisColA 4.3: 3,5,11,13,15,19,21(ans:tftff),23,25(be careful & see prac prob 3!)
Midterm 1: Monday Oct 10, 6-8pm, Steele 006. (Topics: up to Sec 2.3) (solutions)
12 W4.4HW4 due. Coordinate systems and isomorphism. coordsys4.4: 3,7,11,13,15(ans:tff),21,23,27.
14 F4.5Dimension of a vector space or subspace. dimV4.5: 5,7,11,13,19(ans:ttfft),21,23,29(ans:ttt),31.
617 M4.6The Rank Theorem. rankbases 4.6: 1,5,9,15,17(ans:tftft),19,27,29,33.
19 W5.1HW5 due. Eigenvectors and eigenvalues. eigen5.1: 7,9,15,17,20,21(ans:ftttf),23,26(note that A may not be the zero matrix),27,31(find both eigenvalues).
21 F5.2The characteristic equation. chareqn5.2: 3,7,11,15,18,22bcd(ans:ftf),23,25(see Ex.5).
724 M5.3Diagonalization.diagonalization5.3: 5,7,9,13,21(ans:ttff),23,25,27,28.
25 Tu X-hr -practice problem session. xhrmid2prac
26 W4.9, thisHW6 due. App: Markov chains. App: Google PageRank (see links in Resources) code to evolve chain 4.9: 1,5,9,11,19, & writing the A and G matrices for any small web.
Midterm 2: Wednesday Oct 26, 6-8pm, Silsby 028. [make-up slot is Thurs 1-3pm, Haldeman 041] (Topics: Sec. 3.1-5.2) (solutions)
27 Th(4:30pm: colloquium on linear algebra accessible to undergrads)
28 F6.1Inner product, orthogonality. 6.1: 1,5,9,13,19(ans:tttft),24,28,30.
831 M6.2Orthogonal sets. orthog 6.2: 9,11,13,21,23(ans:ttftf),25,28(key),29,33.
Nov 2 W6.3HW7 due. Orthogonal projections. 6.3: 3,7,13,15,17(good),19,22(ans:tttff),23,24.
4 F6.4Constructing orthogonal bases: Gram-Schmidt. (no lecture for Barnett) 6.4: 3,7,9,13,17(ans:ttt),18(ans:ttt),19,21,22.
97 M6.5Least-squares problems. leastsq6.5: 1,5,9,13,17(ans:ttftt),19(lovely),20,21,25.
8 Tu X-hr(Barnett make-up lecture for 6.5)
9 W7.4HW8 due. Singular value decomposition (SVD). 7.4: 3,7,11,13,14(1st row of V^T),18,19,21.
11 F7.4 (7.5 opt)Apps of SVD: fundamental spaces, low rank approximation, principal component analysis (PCA).lowrankapprox.m, image
1014 M-Review.old examsend-of-chapter review probs, make list of topics and problem types, concept maps...
15 THW9 due 8pm (note: not Wed).
Final: Friday Nov 18, 11:30am-2:30pm ("joint math" slot), LSC 100. (solutions)