Homework Problems
Section |
Problems |
1.1 Systems of linear equations |
4, 10, 12, 16, 18, 22, 30 |
1.2 Row reduction and echelon forms |
4, 10, 12, 20, 23, 24 |
1.3 Vector equations |
4, 8, 10, 12, 14, 16, 28, 32 |
1.4 The matrix equation Ax=b |
2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 32, 36 |
1.5 Solution sets of linear systems |
2, 4, 6, 8, 10, 12, 14, 18, 22, 30, 34 |
1.7 Linear independence |
6, 8, 10, 12, 23, 25, 26, 27, 28, 32, 40 |
1.8 Linear transformations |
1, 6, 7, 10, 12, 15, 16, 20, 25, 30, 31 |
2.1 Matrix operations |
1, 3, 6, 7, 8, 9, 12, 18, 19, 22, 24, 27 |
2.2 The inverse of a matrix |
3, 6, 16, 21, 22, 30, 31, 32, 33, 34, 35 |
2.3 Characterizations of invertible matrices |
2, 4, 6, 8, 13, 17, 20, 23, 26 |
3.1 Introduction to determinants |
3, 5, 8, 9, 10, 14, 17, 22, 23, 24, 25, 27, 29, 33, 34, 35, 42 |
3.2 Properties of determinants |
3, 5, 9, 10, 15, 18, 19, 23, 26, 29 |
3.3 Cramer’s rule |
3, 5, 13 |
4.1 Vector spaces and subspaces |
1, 2, 10, 12, 18, 21, 22, 31, 32 |
4.2 Null & column spaces, lin. transformations |
6, 10, 14, 16, 24, 33, 35, 36 |
4.3 Linear independent sets, bases |
4, 6, 8, 10, 14, 16, 20, 23, 24, 29, 30, 31, 32 |
4.5 The dimension of a
vector space |
4, 6, 8, 10, 12, 14, 16, 18, 26, 31 |
4.6 Rank |
2, 4, 6, 8, 10, 12, 14, 16, 20, 29, 30 |
5.1 Eigenvectors and eigenvalues |
2, 4, 6, 8, 12, 14, 16, 18, 24, 26, 29 |
5.2 The characteristic
equation |
4, 8, 12, 14, 16, 20, 23, 24, 25 |
5.3 Diagonalization |
4, 6, 8, 10, 12, 16, 19, 27, 28 |
6.1 Inner product,
length, and orthogonality |
1, 3, 5, 7, 10, 14, 16, 18, 25, 28, 31 |
6.2 Orthogonal sets |
2, 6, 8, 10, 12, 14, 16, 18, 20 |
6.3 Orthogonal projections |
2, 6, 8, 12, 17, 18 |