(pdf files can be read with Acrobat Reader) Review packet of material from previous courses necessary to succeed in Linear Algebra
Pretest for Linear Algebra
Postscript versions of the above files are Review Packet and Pretest
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| 1, 1.5 | 1.1 | Solving linear systems of equations (row reduction) |
| 2 | 1.2 | Echelon Forms of Matrices |
| 3 | 1.3 | Vector Equations |
| 4 | 1.4 | Matrix Equations |
| 5 | 1.5 | Solution Sets of Linear Systems |
| 6 | 1.6 | Linear Independence |
| 7 | 1.7 | Linear Transformations |
| 8 | 1.8 | Matrix of a Linear Transformation |
| 9 | 2.1 | Matrix Operations (multiplication, etc) |
| 10 | 2.2,2.3 | Calculate Matrix Inverse |
| 11 | 2.4 | Partitioned Matrices |
| 12 | 2.5 | Matrix Factorizations (LU-decomposition) |
| 13 | 2.6 | Iterative Solutions of Linear Systems |
| 14 | 2.9 | Subspaces of R^n |
| 15 | 3.1 | Determinants |
| 16 | 3.2 | Properties of Determinants |
| 17 | 4.1 | Vector Spaces and Subspaces |
| 18 | 4.2 | Null space, column space |
| 19 | 4.3 | Bases |
| 20 | 4.4 | Coordinate Systems |
| 21 | 4.5 | Dimension |
| 22 | 4.6 | Rank |
| 23 | 4.7 | Change of Basis |
| 24 | 5.1 | Eigenvectors and Eigenvalues |
| 25 | 5.2 | Characteristic Equation |
| 26 | 5.3 | Diagonalization |
| 27 | 5.4 | Eigenvectors and Eigenvalues |
| 28 | 5.8 | Iterative Estimates for Eigenvalues |
| 29 | 6.1 | Inner Product, length |
| 30 | 6.2 | Orthogonal Sets |
| 31 | 6.3 | Orthogonal Projections |
| 32 | 6.4 | Gram-Schmidt |
| 33 | 6.5 | Least Squares |
| 34 | 6.7 | Inner-Product Space |
| 35 | 7.1 | Diagonalization of Symmetric Matrices |
| 36 | 7.2 | Quadratic Forms |
| 37 | 7.4 | Singular Value Decomposition |