Matrix Methods Files

 

á             Review Sheet 1

á             Practice Examination 1 (link not yet established)

 

 

Matrix Method Homework Assignments

á             Homework Assignments Matrix Methods 2009

á             Homework Assignments Matrix Methods 2009 pdf

 

á             Homework 1 Matrix Manipulation
Homework 2 Matrix Manipulation

á             Homework 3 Partitions, Unit Vectors

á             Homework 4 Vectors

á             Homework 5 Gaussian Elimination

á             Homework 6 Linear Independence

á             Homework 7 Rank

á             Homework 8 Theory of Solutions, Examples

á             Homework 9 Inverses

á             Homework 10 Solving Equations with Inverses

á             Homework 11 Solving Equations using the Inverse

á             Homework 12 LU Decomposition.

 

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Matrix Method Files

 

á                                                  Introduction to Matrices

á                                                  Elementary Matrices

á                                                  Equivalent Systems of Equations

á                                                  Upper Triangular Systems

á                                                  Rank + Nullity

á                                                  Linear Independence

á                                                  Homogeneous Systems

á                                                  Minimal Spanning Sets

á                                                  Row and Column Space

á                                                  LU Factorization

á                                                  Determinants

á                                                  Spectral Mapping Theorem

á                                                  Linear Independent Eigenvectors

á                                                  Projections

á                                                  QR Factorization

á                                                  Traces

á                                                  Cayley-Hamilton Theorem

á                                                  Gram-Schmidt Applications - Fit, Overdetermined, Undetermined Systems

á                                                  Change of Basis

á                                                  Diagonalization of a Self Adjoint Matrix

á                                                   

Homework Solutions

 

Homework 1 Matrix Manipulations

Homework 2 Special Matrices

Homework 3 Partitions, Vectors

Homework 4 Vectors, Gaussian Elimination

Homework 5 Gaussian Elimination, Linear Independence

Homework 6 Rank, Nullity

Homework 7 Theory of Solutions of Linear Equations

Homework 8 Linear Equations

Homework 9 Inverses

Homework 10 Inverses, Solutions of Linear Equations

Homework 11 LU Factorization

Homework 12 Determinants

Homework 13 Adjugate Matrix, CramerÕs Rule

Homework 14 Eigenvalues

Homework 15 Eigenvalues, Eigenvectors

Homework 16, Inner Product, Gram-Schmidt

Homework 17 Projections, QR Factorization, Least Squares

Homework 18 Matrix Functions

Homework 19 Matrix Functions

Homework 20 Diagonalization

Homework 21 Principal Axis Theorem

Homework 22 Change of Basis

Homework 22 errata

Selected Handouts 1999-2000

 

á             Incidence Matrices and Networks

á             Incidence Matrices and Networks Homework Solutions (version 1)

 

á             Least Squares Solutions of Overdetermined Systems

á             Least Squares Solutions of Overdetermined Systems Homework

á                       Solutions

 

á             Bases of a Subspace

á             Basis of a Subspace Homework Solutions

 

á             General Solutions of Linear Equations

á             General Solutions of Linear Equations Homework Solutions

 

á             Rotations

á             Rotations Homework Solutions

 

á             Rayleigh-Ritz Method with Deflation

á             Rayleigh-Ritz Method with Deflation Homework Solutions

 

á             The QR Algorithm

á             The QR Algorithm Homework Solutions

 

á             Matrices on the Calculator

 

á             A Maximal Independent Set of Eigenvectors

 

á             Relaxation Methods

á             Relaxation Methods Homework Solutions

á             Undetermined Coefficients

á             Undetermined Coefficients Homework Solutions