## MAT1341F - Introduction to Linear Algebra
## Final exam solutions## Course MaterialsDiagnostic Test Solutions (note that there was a second version of the test with the same questions but in another order) ## DGD Materials## Announcements## Co-op programThe Co-op program is an exceptional opportunity for students. A co-op job definitely beats working for Macdo or at a night job during the semester. Students can actually earn a living, pay for they studies, get a great work place experience in their field (or at least closely related), start sowing their workplace network, and during the semester actually concentrate on their studies.Here is a link to the Co-op program page. From now until the end of the month, they will be holding information sessions - more info here. ## The Putnam Math CompetitionThe Putnam exam is a north-american wide math exam / contest run out of Harvard. The University of Ottawa participates, and to prepare we hold weekly problem-solving sessions. Any students interested should contact professor Mike Newman by email. To see what kind of problems there are on the exam, check out this link.## Resources### Course NotesHere are some rough class notes from my colleague Barry Jessup. We will more or less be following those notes, so they may be most useful for reading ahead. ### Past ExamsHere is a link to some past exams with solutions. You should try the versions without the solutions before looking at the solutions. ### Linear Algebra Test BankThis is a bank of questions, originally prepared here at the University of Ottawa by Professor Marcel Deruaz and Professor Barry Jessup, edited by Professor Thierry Giordano, Dr. Ana Duff and Dr. Joseph Khoury, and implemented for the web by Dr. Joseph Khoury. I use some of these questions as models when I set multiple choice questions on tests. To use the Linear Algebra test bank, log on to Virtual Campus, choose "Algèbre linéaire - Linear Algebra", and then "projet/project", and you will see a list of links to questions on various topics. ### Math Help CentreThe Math Help Centre, located in Marion 021, is an excellent resource for getting extra help in this course. Here is a link to the Help Centre's webpage with information about which courses they can help with along with hours of operation.
## Suggested Exercises from the Text## Vector Geometry Review and Complex numbers- Section 3.1 - 4a, 6b, 7b, 9b, 10bd, 11, 12b, 13b, 15b, 17dfj, 21
- Section 3.2 - 4bd, 5, 6b, 8bdf, 9df, 10d, 14, 15, 16bdf, 18, 22, 24
- Section 3.3 - 2dfhjl, 3, 4b,7bd,8b, 9, 10bdf, 11, 13bfj, 14b, 16b, 23b, 25
- Section 3.5 - 1b, 3b, 4bd, 5, 8, 9, 10, 20b, plus: show that If u, v, and w are vectors in R3, then u x (v x w)=(u.w)v - (u.v)w, where x denotes the cross product and . the dot product.
- Section 2.5 - 1bfj, 2b, 6b, 7bdf, 8bd, 17, 18, 19, 20bd, 21bd, 25b
- Previous Diagnostic Tests
- Linear Algebra Test Bank: "Vector Geometry" and "Complex Numbers"
## Course Proper- Section 5.1 - 1bdfh, 3bdfh, 4, 5, 7b, 8bdf, 9bdf, 13-17, 21-23, 30
- Section 4.1 - 5bdf, 6bd, [7bd], 8, 9, 10, 13, 17, [18]
- Section 5.2 - 1bdfh, 2bfh, 3ikl, 5, 6ab, [9], 11, 14, 17, [19], 21, 24b[d], 25, [27], 28-30, 35ab
- Section 4.2 - 1abc, 2bd, [4bd], [5bd], 7bdfh, 8, 9b[d], 12-16
- Section 4.3 - 1bd, 2b[d], [3bd], 4, [6bd], 7bd, [8b] , [9bd], 10
- Linear Algebra Test Bank - "Vector Spaces"
- Section 1.1 - 4b, 5, 6, 7, 8b, 10
- Section 1.2 - 1b
- Section 1.3 - 7abc
- Linear Algebra Test Bank - "Linear Systems"
- Section 1.2 - 3b, 4bdfh, [6bdf], 7, 8, 9bd, 12-14a-g[h-j]
- Section 1.3 - 1bdf, 4, 6, 7, 8
- Section 1.4 - 1bdef, 2dh, 6, 7b, 9, 10, 12, 13b, 15, 16, 18, 20, 24b, 29, 31
- Section 1.5 - 2bdf, 5bdf, 8, 9b, 10, 13, 15, 16b, 18c, 20, 21, 24, 26, 27, 31
- Various Sections - 4.1:7bd, 18; 5.2: 9,19, 24bd, 27; 4.2: 4bd, 5bd, 9bd; 4.3: 2bd, 3bd, - 6bd, 8b, 9bd
- Section 4.4 - 1bd, 3b, 4b, 5b, 6b, 7-13, 14*, 15b, 16(done in class)
- Section 4.5 - 1bd, 2b, 3b, 6b, 7bd, 9, 11b, 16, 19, 20
- Section 4.6 - 3 bd, 4b, d (If Ax=b, first find the projection b' of b onto col(A), then solve Ax=b'), 9a, 10
- Section 2.1 - 1bd, 3h, 8, 10bdf, 13bd, 14-16, 20
- Section 2.2 - 4bd, 5, 6, 8ab, 10acdeg, 13, 14b, 19
- Section 2.3 - 2bdf, 4, 5, 6b, 7, 8, 9, 11, 12, 15-17, 21*(more difficult)
- Section 4.9 - 2bd, 3, 4, 5, 12a, 13a, 14b
- Section 5.3 - (In 1, 2 and 12, take V=Rn and W=Rn) 1bdf, 2d, 3a,d, 12
- Linear Algebra Test Bank - "Linear Systems", "Vector Spaces", "Matrix Arithmetic", "Determinants", "Eigenvalues and Diagonalization", and "Linear Transformations"
Everything above here is fair game for the second Midterm. |