18.06SC | Fall 2011 | Undergraduate

# Linear Algebra

## Resource Index

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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 Lecture summary (PDF) Sections 1.1, 1.2, and 2.1 in the 4th or 5th edition

Geometry of Linear Algebra

Problems (PDF)

Solutions (PDF)

An Overview of Key Ideas An Overview of Linear Algebra Lecture summary (PDF)

Sections 1.3 in the 4th or 5th edition

An Overview of Key Ideas None
Elimination with Matrices Lecture: Elimination with Matrices Lecture summary (PDF) Section 2.2 through 2.3 in the 4th or 5th edition Recitation: Elimination with Matrices

Problems (PDF)

Solutions (PDF)

Multiplication and Inverse Matrices Multiplication and Inverse Matrices Lecture summary (PDF) Section 2.4 through 2.5 in the 4th or 5th edition Inverse Matrices

Problems (PDF)

Solutions (PDF)

Factorization into A = LU Factorization into A = LU Lecture summary (PDF) Section 2.6 in the 4th or 5th edition LU Decomposition

Problems (PDF)

Solutions (PDF)

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

Subspaces of Three Dimensional Space

Problems (PDF)

Solutions (PDF)

Column Space and Nullspace Column Space and Nullspace Lecture summary (PDF) Section 3.1 through 3.2 in the 4th or 5th edition Vector Subspaces

Problems (PDF)

Solutions (PDF)

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

Problems (PDF)

Solutions (PDF)

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

Problems (PDF)

Solutions (PDF)

Independence, Basis and Dimension Independence, Basis and Dimension Lecture summary (PDF) Section 3.5 in the 4th edition or Section 3.4 in the 5th edition Basis and Dimension

Problems (PDF)

Solutions (PDF)

The Four Fundamental Subspaces The Four Fundamental Subspaces Lecture summary (PDF) Section 3.6 in the 4th edition or Section 3.5 in the 5th edition Computing the Four Fundamental Subspaces

Problems (PDF)

Solutions (PDF)

Matrix Spaces; Rank 1; Small World Graphs Matrix Spaces; Rank 1; Small World Graphs 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

Problems (PDF)

Solutions (PDF)

Graphs, Networks, Incidence Matrices Graphs, Networks, Incidence Matrices Lecture summary (PDF) Section 8.2 in the 4th edition or Section 10.1 in the 5th edition Graphs and Networks

Problems (PDF)

Solutions (PDF)

Exam 1 Review Exam 1 Review 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 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 Lecture summary (PDF) Section 4.1 in the 4th or 5th edition Problem Solving: Orthogonal Vectors and Subspaces

Problems (PDF)

Solutions (PDF)

Projections onto Subspaces Lecture 15: Projections onto Subspaces Lecture summary (PDF)

Section 4.2 in the 4th or 5th edition

Problem Solving: Projection onto Subspaces

Problems (PDF)

Solutions (PDF)

Projection Matrices and Least Squares Lecture 16: Projection Matrices and Least Squares Lecture summary (PDF) Section 4.3 in the 4th or 5th edition Problem Solving: Least Squares Approximation

Problems (PDF)

Solutions (PDF)

Orthogonal Matrices and Gram-Schmidt Lecture 17: Orthogonal Matrices and Gram-Schmidt Lecture summary (PDF) Section 4.4 in the 4th or 5th edition Problem Solving: Gram-Schmidt Orthogonalization

Problems (PDF)

Solutions (PDF)

Properties of Determinants Lecture 18: Properties of Determinants Lecture summary (PDF) Section 5.1 in the 4th or 5th edition Problem Solving: Properties of Determinants

Problems (PDF)

Solutions (PDF)

Determinant Formulas and Cofactors Lecture 19: Determinant Formulas and Cofactors Lecture summary (PDF) Section 5.2 in the 4th or 5th edition

Problem Solving: Determinants

Problems (PDF)

Solutions (PDF)

Cramer’s Rule, Inverse Matrix and Volume Lecture 20: Cramer’s Rule, Inverse Matrix and Volume Lecture summary (PDF) Section 5.3 in the 4th or 5th edition

Problem Solving: Determinants and Volume

Problems (PDF)

Solutions (PDF)

Eigenvalues and Eigenvectors Lecture 21: Eigenvalues and Eigenvectors Lecture summary (PDF) Section 6.1 through 6.2 in the 4th or 5th edition Problem Solving: Eigenvalues and Eigenvectors

Problems (PDF)

Solutions (PDF)

Diagonalization and Powers of A Lecture 22: Diagonalization and Powers of A Lecture summary (PDF) Section 6.2 in the 4th or 5th edition Problem Solving: Powers of a Matrix

Problems (PDF)

Solutions (PDF)

Differential Equations and exp(At) Lecture 23: Differential Equations and exp(At) Lecture summary (PDF) Section 6.3 in the 4th or 5th edition

Problem Solving: Determinants and VolumeDifferential Equations and exp(At)

Problems (PDF)

Solutions (PDF)

Markov Matrices; Fourier Series Lecture 24: Markov Matrices; Fourier Series Lecture summary (PDF) Section 8.3 and 8.5 in the 4th edition or Sections 10.3 and 10.5 in the 5th edition Problem Solving: Markov Matrices

Problems (PDF)

Solutions (PDF)

Exam 2 Review Exam 2 Review

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

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 Lecture 25: Symmetric Matrices and Positive Definiteness Lecture summary (PDF) Section 6.4 through 6.5 in the 4th or 5th edition Problem Solving: Symmetric Matrices and Positive Definiteness

Problems (PDF)

Solutions (PDF)

Complex Matrices; Fast Fourier Transform (FFT) Lecture 26: Complex Matrices; Fast Fourier Transform (FFT) Lecture summary (PDF)

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

Problem Solving: Complex Matrices

Problems (PDF)

Solutions (PDF)

Positive Definite Matrices and Minima Lecture 27: Positive Definite Matrices and Minima Lecture summary (PDF) Section 6.5 in the 4th or 5th edition Problem Solving: Positive Definite Matrices and Minima

Problems (PDF)

Solutions (PDF)

Similar Matrices and Jordan Form Lecture 28: Similar Matrices and Jordan Form Lecture summary (PDF) Section 6.6 in the 4th edition or Section 6.2 in the 5th edition Problem Solving: Similar Matrices

Problems (PDF)

Solutions (PDF)

Singular Value Decomposition Lecture 29: Singular Value Decomposition Lecture summary (PDF) Section 6.7 in the 4th edition or Section 7.1 and 7.2 in the 5th edition Problem Solving: Determinants and VolumeComputing the Singular Value Decomposition

Problems (PDF)

Solutions (PDF)

Linear Transformations and their Matrices Lecture 30: Linear Transformations and their Matrices Lecture summary (PDF) Section 7.1 in the 4th edition or Section 8.1 in the 5th edition Problem Solving: Linear Transformations

Problems (PDF)

Solutions (PDF)

Change of Basis; Image Compression Lecture 31: Change of Basis; Image Compression Lecture summary (PDF) Section 7.2 in the 4th edition or Section 8.2 in the 5th edition Problem Solving: Change of Basis

Problems (PDF)

Solutions (PDF)

Left and Right Inverses; Pseudoinverse Lecture 33: Left and Right Inverses; Pseudoinverse Lecture summary (PDF) Section 7.3 in the 4th edition or Section 8.3 in the 5th edition Problem Solving: Pseudoinverses

Problems (PDF)

Solutions (PDF)

Exam 3 Review Exam 3 Review 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 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 Lecture summary (PDF) None  Final Exam Problem Solving None

### Final Exam

FINAL EXAM EXAMS AND SOLUTIONS
Final Exam

Exams (PDF)

Solutions (PDF)

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## Course Info

Fall 2011
##### Learning Resource Types
Lecture Videos
Exams with Solutions
Lecture Notes
Recitation Videos
Problem Sets with Solutions
Simulations
Course Introduction
Instructor Insights