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 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
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
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
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
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