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