SyDe114 - Linear Algebra
Assignments and Solutions
Assignments and Solutions
Stephen
Birkett
|
SyDe114 - Linear Algebra Assignments and Solutions |
Stephen
Birkett
|
Research
Teaching
Linear Algebra
Topics and Lectures Assignments Mini-Tests Numerical Methods Computational Mathematics Musical Instruments Music
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Suggest assigned problems and links to solutions are listed below for each unit. I may add to this list, or adjust it to fine tune, as we proceed with the course. So check back here regularly. References are to Schaum's Outline, Linear Algebra, 3rd Edition, 2001. Try doing the problems before looking at the solutions! | ||||||
| UNIT 1 - VECTOR SPACES | |||||||
vector space
axioms
| 4.71-73 | ||||||
| Euclidean spaces | 1.41ab, 1.43ab, 1.46, 1.47 | ||||||
| complex numbers | 1.66-69, 1.70abc | ||||||
| subspaces | 4.75, 4.77, 4.78, 4.80-82 | ||||||
| linear combinations | 4.83-85 | ||||||
| linear independence | 4.89-91, 4.93 | ||||||
| basis & dimension | 4.97, 4.98, 4.101-103 | ||||||
| matrix rank, rowspace | 4.104-4.113 | ||||||
| coordinates | 4.128-133 | ||||||
| miscellaneous | 4.134-136 | ||||||
UNIT 2 - MATRIX ALGEBRA | |||||||
| matrix multiplication | 2.38, 2.39,2.50 | ||||||
| inverses | 2.53, 2.54, 3.67[use row reduction method] | ||||||
| echelon, row-canonical | 3.62 | ||||||
| elementary matrices | 3.65, 3.66 | ||||||
| determinants | 8.38ace, 8.40ab, 8.41, 8.43a | ||||||
| cofactors/adjoint | 8.44 | ||||||
UNIT 3 - LINEAR MAPS | |||||||
| linear maps | 5.49, 5.50bd, 5.51-5.53, 5.56b, 5.57b, 5.58b, 5.70, 5.71 | ||||||
| kernel & image | 5.61, 5.62bc, 5.63-5.667 | ||||||
| invertible & nonsingular maps | 5.56a, 5.57a, 5.58a, 5.76, 5.79, 5.80 | ||||||
| matrix representations | 6.37-6.42 | ||||||
| change of basis | 6.47d, 6.48-6.50 | ||||||
| matrix rep & change of basis | 6.52, 6.53, 6.54a, 6.55, 6.56ac, 6.59 | ||||||
UNIT 4 - EIGENVALUES, EIGENVECTORS & DIAGONALIZATION | |||||||
| eigenvalues & eigenvectors | 9.45ab, 9.46, 9.48, 9.49, 9.51, 9.53, 9.54 | ||||||
UNIT 5 - INNER PRODUCT SPACES & ORTHOGONALITY | |||||||
| inner products | 7.57, 7.59, 7.60b, 7.62 | ||||||
| applications in Rn | 1.41, 1.43, 1.44c, 1.45 | ||||||
| applications in Cn | 7.91-7.93 | ||||||
| lines & planes | 1.51, 1.52, 1.55 [and distance Q to H], 1.62, 1.64 | ||||||
| orthogonality | 7.64, 7.66-7.69 | ||||||
| orthogonal projection & bases | 7.74bc, 7.75-7.77, 7.94 | ||||||
| orthogonal matrices | 7.81, 9.56bc, 9.57a | ||||||
UNIT 6 - LINEAR SYSTEMS | |||||||
| homogeneous systems | 3.57-3.60 ,4.99b,4.100b | ||||||
| equations of a line in Rn | 1.53, 1.56 | ||||||
| non-homogeneous systems | 3.52ab,3.53-3.56 | ||||||
