# Prep 2011 workshop Linear Algebra Assignment Status

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## Current status of Linear Algebra Model Course Assignments[edit]

Topic | NPL | Custom | Header | Updated | Notes | |
---|---|---|---|---|---|---|

Vectors
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Dot product and Vector Projections | 15 | 2011-06-25 | ||||

Geometric objects - lines and planes | 14 | X | 2011-06-25 | This set could use some work in connecting to linear algebra. For example given standard equation of plane, find parametric equations | ||

Orthogonal decomposition | ||||||

Systems of equations and elimination
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Row operations and Row Echelon Form | 11 | X | 2011-06-25 | |||

Gaussian elimination (Free variables & Consistency of solutions) | 27 | X | 2011-06-25 | |||

Rank of a Matrix | 2 | 2011-06-26 | There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations | |||

Matrix operations and algebra
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Matrix arithmetic | 15 | 1 | X | 2011-06-25 | ||

Matrix inverse | 17 | X | 2011-06-26 | |||

Matrix equations | 5 | X | 2011-06-25 | |||

Determinant and Cramer's Rule | 30 | 1 | X | 2011-06-26 | Need to add Cramer's rule Qs | |

Elementary matrices and LU Decomposition | 3 | 2 | X | 2011-06-25 | There are determinant of elementary matrix questions in the NPL in Linear Algebra/Matrices/Determinants | |

Vector space preliminaries
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Definition of a vector space and subspaces | 8 | X | 2011-06-26 | |||

Euclidean vector spaces | 4 | 2011-06-25 | ||||

Linear combinations and span | 14 | X | 2011-06-26 | |||

Linear independence | 13 | X | 2011-06-26 | |||

Basis and dimension | 26 | X | 2011-07-22 | Several problems say "kernel" and "image." Change to Column space & null space? Or include both in some/all? Need some Rank and Nullity questions? | ||

Coordinate vectors and change of basis | Not finding problems in NPL yet | |||||

Row space, column space, and null space. Rank and Nullity | 0 | X | 2011-07-22 | This set was deleted by JF since it is redundant with 45_Basis and Dimension. | ||

Geometric examples | ||||||

Linear transformations
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Definition of a linear transformation | 5 | 2011-06-26 | The NPL needs a few more problems | |||

Matrix of a linear transformation | 18 | 2011-06-26 | There are some problems in the NPL on transformation of vector spaces of matrices, but not included in model course. There are some more abstract problems that could go into chapter 6 | |||

Reflections, rotations, dilations and projections | 9 | |||||

Inverse of a transformation | 4 | 2011-07-11 | NPL has only a few problems | |||

Kernel, range, injection, surjection | 11 | 2011-07-11 | ||||

Applications
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Graph Theory | 1 | 2011-07-22 | NPL needs a couple more new problems for example Incidence matrix. Name changed from "Adjancency Matrix" to allow more problems. | |||

Least squares Approximation | 2 | 2011-08-09 | Some problems have awkward wording could use some editing. New problem were added by JF July 25 and Aug 9. | |||

Mixture problems | ||||||

Simplex method | ||||||

Approximation of a function by a Fourier polynomial | ||||||

Quadratic Forms | ||||||

Eigenvalues and eigenvectors
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Finding eigenvalues and eigenvectors | 12 | 2011-06-25 | ||||

Eigenspaces | 2011-06-25 | |||||

Diagonalization | 2011-06-25 | |||||

Symmetric matrices & Trace | 2011-06-25 | There are some "trace" problems in the NPL in Linear Algebra/Matrices/Matrix Operations | ||||

Quadratic forms | 2011-06-25 | |||||

Inner product spaces and abstract vector spaces
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Inner Product Spaces, Length, Orthogonality | ||||||

Orthonormal Bases | ||||||

Orthogonal Projections. Orthogonal Complements | ||||||

Gram-Schmidt Process | 2011-06-25 | |||||

QR Factorization | ||||||

Diagonalization of Symmetric Matrices | ||||||

Singular Value Decomposition | ||||||