## Linear Algebra 2019 Spring

The material on this webspage accompanies the course MATH2418.006 at The University of Texas at Dallas.

### Textbook:

• Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, Wellesley-Cambridge Press, 2017. ISBN: 978-09802327-7-6.
• Howard Anton, Elementary Linear Algebra, Wiley 11th Edition, 2013. ISBN: 978-1-118-47350-4.

### Lecture Notes and Homework:

• Introduction to Vectors

• Solving Linear Equations

• Vectors and Linear Equations [pdf]
• The Idea of Elimination [pdf]
• Elimination Using Matrices [pdf]
• Rules for Matrix Operations[pdf]
• Inverse Matrices [pdf]
• Elimination = Factorization: A = LU [pdf]
• Transposes and Permutations [pdf]

• Homework 3 [pdf] and Solutions [pdf]
• Homework 4 [pdf] and Solutions [pdf]
• Homework 5 [pdf] and Solutions [pdf]
• Vector Spaces and Subspaces

• Spaces of Vectors [pdf]
• NullSapce of A: Solving Ax = 0 and Rx = 0 [pdf]
• The Complete Solution to Ax = b [pdf]
• Independence, Basis and Dimension [pdf]
• Dimensions of the Four Subspaces [pdf]

• Homework 6 [pdf] and Solutions [pdf]
• Homework 7 [pdf] and Solutions [pdf]
• Homework 8 [pdf] and Solutions [pdf]
• Orthogonality

• Orthogonality of the Four Subspaces [pdf]
• Projections [pdf]
• Least Squares Approximations [pdf]
• Orthonormal Bases and Gram-Schmidt [pdf]

• Homework 9 [pdf] and Solutions [pdf]
• Determinants

• The Properties of Determinants [pdf]
• Permutations and Cofactors [pdf]
• Cramer's Rule, Inverses, and Volumes [pdf]

• Homework 10 [pdf] and Solutions [pdf]
• Homework 11 [pdf] and Solutions [pdf]
• Eigenvalues and Eigenvectors

• Introduction to Eigenvalues [pdf]
• Diagonalizing a Matrix [pdf]
• Symmetric Matrices [pdf]
• Positive Definite Matrices [pdf]

• Homework 12 [pdf] and Solutions [pdf]
• The Singular Value Decomposition (SVD)

• Bases and Matrices in the SVD [pdf]

• Extra Problems for section 6.5 and 7.2 [pdf] and Solutions [pdf]