# Resource Index « Previous »

This resource index gives users access to most of the course resources in a single location.

## Unit I: Ax = b and the Four Subspaces

TITLES LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SOLVING VIDEOS PROBLEM SETS
The Geometry of Linear Equations The Geometry of Linear Equations (00:39:49) Lecture summary (PDF) Sections 1.1, 1.2, and 2.1 in the 4th or 5th edition

Geometry of Linear Algebra (00:16:35)

Problems (PDF)

Solutions (PDF)

An Overview of Key Ideas An Overview of Linear Algebra (00:49:32) Lecture summary (PDF)

Sections 1.3 in the 4th or 5th edition

An Overview of Key Ideas (00:07:42) None
Elimination with Matrices Elimination with Matrices (00:47:42) Lecture summary (PDF) Section 2.2 through 2.3 in the 4th or 5th edition Elimination with Matrices (00:10:13)

Problems (PDF)

Solutions (PDF)

Multiplication and Inverse Matrices Multiplication and Inverse Matrices (00:46:49) Lecture summary (PDF) Section 2.4 through 2.5 in the 4th or 5th edition Inverse Matrices (00:08:24)

Problems (PDF)

Solutions (PDF)

Factorization into A = LU Factorization into A = LU (00:50:13) Lecture summary (PDF) Section 2.6 in the 4th or 5th edition LU Decomposition (00:09:33)

Problems (PDF)

Solutions (PDF)

Transposes, Permutations, Vector Spaces Transposes, Permutations, Vector Spaces (00:47:42) Lecture summary (PDF) Section 2.7 in the 4th or 5th edition

Subspaces of Three Dimensional Space (00:14:44)

Problems (PDF)

Solutions (PDF)

Column Space and Nullspace Column Space and Nullspace (00:46:01) Lecture summary (PDF) Section 3.1 through 3.2 in the 4th or 5th edition Vector Subspaces (00:08:45)

Problems (PDF)

Solutions (PDF)

Solving Ax = 0: Pivot Variables, Special Solutions Solving Ax = 0: Pivot Variables, Special Solutions (00:43:20) Lecture summary (PDF) Section 3.2 in the 4th or 5th edition Solving Ax=0 (00:10:03)

Problems (PDF)

Solutions (PDF)

Solving Ax = b: Row Reduced Form R Solving Ax = b: Row Reduced Form R (00:47:20) Lecture summary (PDF) Section 3.3 through 3.4 in the 4th or 5th edition Solving Ax=b (00:09:03)

Problems (PDF)

Solutions (PDF)

Independence, Basis and Dimension Independence, Basis and Dimension (00:50:14) Lecture summary (PDF) Section 3.5 in the 4th edition or Section 3.4 in the 5th edition Basis and Dimension (00:08:09)

Problems (PDF)

Solutions (PDF)

The Four Fundamental Subspaces The Four Fundamental Subspaces (00:49:20) Lecture summary (PDF) Section 3.6 in the 4th edition or Section 3.5 in the 5th edition Computing the Four Fundamental Subspaces (00:10:44)

Problems (PDF)

Solutions (PDF)

Matrix Spaces; Rank 1; Small World Graphs Matrix Spaces; Rank 1; Small World Graphs (00:45:56) Lecture summary (PDF) Section 3.3 and 8.2 in the 4th edition or Section 3.3 and 10.1 in the 5th edition Matrix Spaces (00:08:55)

Problems (PDF)

Solutions (PDF)

Graphs, Networks, Incidence Matrices Graphs, Networks, Incidence Matrices (00:47:57) Lecture summary (PDF) Section 8.2 in the 4th edition or Section 10.1 in the 5th edition Graphs and Networks (00:12:30)

Problems (PDF)

Solutions (PDF)

Exam 1 Review Exam 1 Review (00:47:40) Lecture summary (PDF) Review Chapters 1, 2, and 3, plus Section 8.2 in the 4th edition or Chapters 1, 2, and 3, plus Section 10.1 in the 5th edition Exam 1 Problem Solving (00:14:52) None

## Exam 1

EXAM EXAMS AND SOLUTIONS
Exam 1

Exams (PDF)

Solutions (PDF)

## Unit II: Least Squares, Determinants and Eigenvalues

TITLES LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SOLVING VIDEOS PROBLEM SETS
Orthogonal Vectors and Subspaces Orthogonal Vectors and Subspaces (00:49:48) Lecture summary (PDF) Section 4.1 in the 4th or 5th edition Orthogonal Vectors and Subspaces (00:10:19)

Problems (PDF)

Solutions (PDF)

Projections onto Subspaces Projections onto Subspaces (00:48:51) Lecture summary (PDF)

Section 4.2 in the 4th or 5th edition

Projection onto Subspaces (00:09:50)

Problems (PDF)

Solutions (PDF)

Projection Matrices and Least Squares Projection Matrices and Least Squares (00:48:05) Lecture summary (PDF) Section 4.3 in the 4th or 5th edition Least Squares Approximation (00:08:03)

Problems (PDF)

Solutions (PDF)

Orthogonal Matrices and Gram-Schmidt Orthogonal Matrices and Gram-Schmidt (00:49:25) Lecture summary (PDF) Section 4.4 in the 4th or 5th edition Gram-Schmidt Orthogonalization (00:09:59)

Problems (PDF)

Solutions (PDF)

Properties of Determinants Properties of Determinants (00:49:12) Lecture summary (PDF) Section 5.1 in the 4th or 5th edition Properties of Determinants (00:09:55)

Problems (PDF)

Solutions (PDF)

Determinant Formulas and Cofactors Determinant Formulas and Cofactors (00:53:17) Lecture summary (PDF) Section 5.2 in the 4th or 5th edition

Determinants (00:12:48)

Problems (PDF)

Solutions (PDF)

Cramer's Rule, Inverse Matrix and Volume Cramer's Rule, Inverse Matrix and Volume (00:51:01) Lecture summary (PDF) Section 5.3 in the 4th or 5th edition

Determinants and Volume (00:13:49)

Problems (PDF)

Solutions (PDF)

Eigenvalues and Eigenvectors Eigenvalues and Eigenvectors (00:51:23) Lecture summary (PDF) Section 6.1 through 6.2 in the 4th or 5th edition Eigenvalues and Eigenvectors (00:09:21)

Problems (PDF)

Solutions (PDF)

Diagonalization and Powers of A Diagonalization and Powers of A (00:51:50) Lecture summary (PDF) Section 6.2 in the 4th or 5th edition Powers of a Matrix (00:09:06)

Problems (PDF)

Solutions (PDF)

Differential Equations and exp(At) Differential Equations and exp(At) (00:51:03) Lecture summary (PDF) Section 6.3 in the 4th or 5th edition

Differential Equations and exp(At) (00:10:19)

Problems (PDF)

Solutions (PDF)

Markov Matrices; Fourier Series Markov Matrices; Fourier Series (00:51:12) Lecture summary (PDF) Section 8.3 and 8.5 in the 4th edition or Sections 10.3 and 10.5 in the 5th edition Markov Matrices (00:11:48)

Problems (PDF)

Solutions (PDF)

Exam 2 Review Exam 2 Review (00:48:20)

Lecture summary (PDF) Review Chapters 4, 5, and 6 (through Sec. 6.3) plus Sections 8.3 and 8.5 in the 4th edition or Review Chapters 4, 5, and 6 (through Sec. 6.3) plus Sections 10.3 and 10.5 in the 5th edition

Exam 2 Problem Solving (00:17:51)

None

## Exam 2

EXAM EXAMS AND SOLUTIONS
Exam 2

Exams (PDF)

Solutions (PDF)

## Unit III: Positive Definite Matrices and Applications

TITLES LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SOLVING VIDEOS PROBLEM SETS
Symmetric Matrices and Positive Definiteness Symmetric Matrices and Positive Definiteness (00:43:52) Lecture summary (PDF) Section 6.4 through 6.5 in the 4th or 5th edition Symmetric Matrices and Positive Definiteness (00:13:05)

Problems (PDF)

Solutions (PDF)

Complex Matrices; Fast Fourier Transform (FFT) Complex Matrices; Fast Fourier Transform (FFT) (00:47:52) Lecture summary (PDF)

Section 10.2 through 10.3 in the 4th edition or Section 9.2 and 9.3 in the 5th edition

Complex Matrices (00:13:00)

Problems (PDF)

Solutions (PDF)

Positive Definite Matrices and Minima Positive Definite Matrices and Minima (00:50:40) Lecture summary (PDF) Section 6.5 in the 4th or 5th edition Positive Definite Matrices and Minima (00:12:49)

Problems (PDF)

Solutions (PDF)

Similar Matrices and Jordan Form Similar Matrices and Jordan Form (00:45:56) Lecture summary (PDF) Section 6.6 in the 4th edition or Section 6.2 in the 5th edition Similar Matrices (00:08:12)

Problems (PDF)

Solutions (PDF)

Singular Value Decomposition Singular Value Decomposition (00:41:35) Lecture summary (PDF) Section 6.7 in the 4th edition or Section 7.1 and 7.2 in the 5th edition Computing the Singular Value Decomposition (00:11:35)

Problems (PDF)

Solutions (PDF)

Linear Transformations and their Matrices Linear Transformations and their Matrices (00:49:27) Lecture summary (PDF) Section 7.1 in the 4th edition or Section 8.1 in the 5th edition Linear Transformations (00:10:46)

Problems (PDF)

Solutions (PDF)

Change of Basis; Image Compression Change of Basis; Image Compression (00:50:14) Lecture summary (PDF) Section 7.2 in the 4th edition or Section 8.2 in the 5th edition Change of Basis (00:12:25)

Problems (PDF)

Solutions (PDF)

Left and Right Inverses; Pseudoinverse Left and Right Inverses; Pseudoinverse (00:41:53) Lecture summary (PDF) Section 7.3 in the 4th edition or Section 8.3 in the 5th edition Pseudoinverses (00:14:39)

Problems (PDF)

Solutions (PDF)

Exam 3 Review Exam 3 Review (00:47:06) Lecture summary (PDF) Review Chapters 6 and 7, plus Sections 10.2 through 10.3 in the 4th edition or Review Chapters 6, 7, and 8 plus Sections 9.2 through 9.3 in the 5th edition Exam 3 Problem Solving (00:12:49) None

## Exam 3

EXAM EXAMS AND SOLUTIONS
Exam 3

Exams (PDF)

Solutions (PDF)

## Final Course Review

TITLES LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SOLVING VIDEOS PROBLEM SETS
Final Course Review   Final Course Review (00:43:25) Lecture summary (PDF) None   Final Exam Problem Solving (00:12:16) None

## Final Exam

FINAL EXAM EXAMS AND SOLUTIONS
Final Exam

Exams (PDF)

Solutions (PDF)

« Previous »