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Chapter 1
o 1.1 Systems of Linear Equations Sec 1.1
o 1.2 Row Reduction and Echelon Form Sec 1.2
o 1.3 Vectors and Vector equations Sec 1.3
o 1.4 The matrix-vector products Sec 1.4
o 1.5 Solution sets of linear systems Sec 1.5
o 1.6 Applications Sec 1.6
o 1.7 Linear Independence Sec 1.7
o 1.8 Linear transformations Sec 1.8
o 1.9 Matrix representations of Linear transformation Sec 1.9
Chapter 2
o 2.1 Matrix algebra Sec 2.1
o 2.2 The inverse of a matrix Sec 2.2
o 2.3 Properties of invertible matrices Sec 2.3
o 2.7 Applications to computer graphics Sec 2.7
o 2.8 Subspaces, column space, null space, and basis. Sec 2.8
o 2.9 Dimension and rank Sec 2.9
Chapter 3
o 3.1 Determinants Sec 3.1
o 3.2 Determinants and their properties Sec 3.2
o 3.3 Applications of determinants: Cramer’s Rule Sec 3.3
Chapter 5
o 5.1 Eigenvalues and eigenvectors Sec 5.1
o 5.2/5.3 The characteristic equation, Diagonalization Sec
5.2-5.3
o 5.5 Complex eigenvalues Sec 5.5
o 5.6 Discrete dynamical systems Sec 5.6
Chapter 6
o 6.1 Inner product, length, orthogonality Sec 6.1
o 6.2/6.3 Orthogonal sets, Orthogonal projections Sec
6.2-6.3
o 6.5 Least squares Sec 6.5
Chapter 7
o 7.1 Diagonalization of symmetric matrices Sec 7.1