lecture  week  date  reading, reminders  daily topics  section 1 resources  section 2 resources  practice problems from book 

#1  0  June 23 F  website, 1.1  Systems of linear equations  solnsets worksheet  lecture01.pdf  5, 7, 9, 11, 13, 21, 27 
#2  June 24 Sa  1.2  Row reduction, echelon forms  row reduction, echelon form examples; echform worksheet 
lecture02.pdf
1;4205;0c classwork02.pdf 
3, 5, 13, 15, 19, 21(ans:ffttf), 31  
#3  1  June 26 M  1.3  Vector equations, linear combinations, span  span worksheets: from class, another  lecture03.pdf  7, 9, 11, 15, 21, 22, 23(ans:ffttf) 
#4  June 28 W  1.4, 1.5  The matrix equation Ax=b, solution sets  matvec  lecture04.pdf  1.4: 3, 9, 15, 19, 23(ans:ftfttt) 1.5: 7, 15, 23(ans:tffft), 27, 31 

#5  June 30 F  1.6, 1.7, HW1 Due  Linear independence, Applications: network flow  lecture05.pdf  1.6: 11, 12 1.7: 5, 13, 17, 21(ans:fftt), 25, 27, 33, 37, 39 

Xhour  Resources on proofs  doing proofs  methods of proof  lectureX01.pdf  
#6  2  July 3 M  1.8  Introduction to linear transformations 
lecture06.pdf
classwork06.pdf classwork06ans.pdf linxform 
lecture06.pdf
classwork06.pdf classwork06ans.pdf 
7, 9, 11, 13, 17, 19, 21(ans:tffft), 27 
#7  July 5 W  1.9  The matrix of a linear transformation  onto and 11 
lecture07.pdf
classwork07.pdf classwork07ans.pdf 
3, 9, 15, 17, 23(ans:ttfff)), 25, 35.  
#8  July 7 F  1.10, 2.1  HW2 Due. Applications: difference equations, matrix operations  matrix multiplication  lecture08.pdf  1.10: 9. 2.1: 3,5,9,15(ans:ffttf),16(ans:ftfft),17,21(tricky),23.  
Xhour  Resources on proofs 
more critical thinking about proofs
No Xhour for section 2 this week (they are welcome in section 1) 
1x1 lin sys proofs, Is it a proof?  
#9  3  July 10 M  2.2  The inverse of a matrix  basic inverse computation  lecture09.pdf  7, 10(ans:ftttf), 13, 17, 19, 21, 31, 35 
#10  July 12 W  2.3  Characteristics of invertible matrices  (exercise proving p.114 of book)  lecture11.pdf  3,7,11(ans:ttftt),15,17,22,27,33.  
#12  July 14 F  4.1, HW3 Due  Vector spaces and subspaces  subspace  lecture12.pdf  2,3,7,9,15,17,31  
Xhour (#11)  3.1, 3.2  Extra lecture (a oneoff): Determinants and their properties (for section 2: Xhr is Tuesday so lecs #10 and #11 swapped)  det via row red.  lecture10x.pdf  3.1: 5,9,11,35,37; 3.2: 7,23,27(ans:tftf),29,31,33,39  
#13  4  July 17 M  4.2  Null and column spaces  lecture13.pdf  3, 7, 11, 17, 21, 23, 25(ans:tftftt). [For some harder ones: 31, 35]  
#14  July 19 W  4.3  Bases, spanning set theorem  lecture14.pdf  3,5,11,13,15,19,21(ans:tftff),23,25(be careful & see prac prob 3!)  
Midterm 1: Wednesday July 19, 6:00pm  8:00pm, Kemeny 008 (solutions)  
#15  July 21 F  4.4, HW4 Due  Coordinate systems and isomorphism  basis for Col A 
lecture15.pdf classwork15.pdf 
3,7,11,13,15(ans:tff),21,23,27  
Xhour 
m22matlab.m m22sagenotebook sagequickref.pdf sageforlinearalgebra.pdf 

#16  5  July 24 M  4.5  Dimension of a vector space or subspace  dimension of subspaces of R3 worksheet  lecture16.pdf  5,7,11,13,19(ans:ttfft),21,23,29(ans:ttt),31 (ie T cannot grow the dim!) 
#17  July 26 W  4.6  The rank theorem  abstract V.S. review, rank and bases worksheet  lecture17.pdf  4.6: 1,5,9,15,17(ans:tftft),19,27,29,33  
#18  July 28 F  5.1, HW5 Due  Eigenvectors and eigenvalues  eigen worksheet  lecture18.pdf  5.1: 7,9,15,17,20,21(ans:ftttf),23,26(note that A may not be the zero matrix),27,31(find both eigenvalues)  
Xhour  Resources  Linear algebra on the computer, MATLAB  No Xhour for section 2  
#19  6  July 31 M  5.2  The characteristic equation  (Quiz 2 for section 1). char eqn (use for practise)  lecture19.pdf  5.2: 3,7,11,15,18,22bcd(ans:ftf),23,25(see Ex.5) 
#20  Aug 2 W  5.3  Diagonalization  diagonalization  lecture20.pdf  5.3: 5,7,9,13,21(ans:ttff),23,25,27,28  
#21  Aug 4 F  4.9, Resources, HW6 Due  Applications: Markov chains, Google PageRank  evolve.m 
lecture21.pdf
PageRank2x2 PageRank3x3 PageRank4x4 
4.9: 1,5,9,11,19, & writing the A and G matrices for any small web.  
Xhour  mathematical language grammar worksheet, mid2 prac qus  (Quiz for section 2)  
#22  7  Aug 7 M  6.1  Inner products, orthogonality  lecture22.pdf  6.1: 1,5,9,13,19(ans:tttft),24,28,30.  
Midterm 2: Tuesday August 8, 6:00pm  8:00pm, Kemeny 008 (solutions)  
#23  Aug 9 W  6.2  Orthogonal sets  orthog sets worksheet  lecture23.pdf  6.2: 9,11,13,21,23(ans:ttftf),25,28(key),29,33.  
#24  Aug 11 F  6.3, HW7 Due  Orthogonal projections  lecture24.pdf  6.3: 3,7,13,15,17(good),19,22(ans:tttff),23,24  
Xhour  
#25  8  Aug 14 M  6.4  Constructing orthogonal bases: GramSchmidt  Guest lecture: Lizzie Tripp 
Guest lecture: Emma Hartman
classwork25.pdf 
6.4: 3,7,9,13,17(ans:ttt),18(ans:ttt),19,21,22. 
#26  Aug 16 W  6.5  Leastsquares problems  least sq worksheet  lecture26.pdf  6.5: 1,5,9,13,17(ans:ttftt),19(lovely; note b has a vector 0 that should be a scalar 0),20,21,25.  
#27  Aug 18 F  7.4, HW8 Due  Singular value decomposition (SVD) 
lecture27.pdf
SVD2x2 
7.4: 3,7,11,13,14(1st row of V^T),18,19,21.  
Xhour  Guest lecture: Lizzie Tripp (7.1 and trace formula for graphs)  
#28  9  Aug 21 M  7.4, 7.5  Applications of SVD: fundamental spaces, low rank approximation, principal component analysis (PCA)  lowrankapprox.m demo, needs mystery.jpg  lecture28.pdf  
Xhour  Guest lecture: Emma Hartman  
#29  Aug 23 W  HW9 Due  Review  review diag/orthog 
lecture29.pdf
classwork29.pdf classwork29ans.pdf 

Final Exam (Section 1): Monday August 28, 8:00am11:00am, location Kemeny 008 (solutions)  
Final Exam (Section 2): Sunday August 27, 8:00am11:00am, location Kemeny 006 (solutions) 