Prep 2011 workshop Linear Algebra Assignment Status
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Current status of Linear Algebra Model Course Assignments
Topic | NPL | Custom | Header | Updated | Notes | |
---|---|---|---|---|---|---|
Vectors | ||||||
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 | ||||||
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 | ||||||
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 | ||||||
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 | 2011-06-26 | ||||
Coordinate vectors and change of basis | ||||||
Row space, column space, and null space. Rank and Nullity | 7 | 2011-06-26 | 5 problems say "kernel" and "image." Change to Column space & null space? Or include both in some/all. | |||
Geometric examples | ||||||
Linear transformations | ||||||
Definition of a linear transformation | 1 | 2011-06-26 | The NPL needs more problems | |||
Matrix of a linear transformation | 16 | 2011-06-26 | There are some problems in the NPL on transformation of vector spaces of matrices, but not included in model course | |||
Reflections, rotations, dilations and projections | 9 | |||||
Inverse of a transformation | ||||||
Kernel, range, injection, surjection | ||||||
Applications | ||||||
Adjacency matrix | 1 | X | 2011-06-26 | NPL needs a couple more new problems | ||
Least squares Approximation | Some problems have awkward wording could use some editing | |||||
Curve/surface fitting | ||||||
Mixture problems | ||||||
Simplex method | ||||||
Graph theory | Should probably put the adjancency matrix problem here and delete adjancency matrix subsection | |||||
Approximation of a function by a Fourier polynomial | ||||||
Quadratic Forms | ||||||
Eigenvalues and eigenvectors | ||||||
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 | ||||||
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 | ||||||