Aaron Bagheri

Graduate Student, Mathematics

University of California, Santa Barbara


Math 4A!

Credit for most of these PDFs goes to Micah Pedrick . If you appreciate these, let me know so I can let him know!


Worksheets

1.1 - Systems of Linear Equations:

1.2 - Row Reduction:

1.3 - Vector Equations:

1.4 - Matrix-Vector Products:

1.5 - Solution Sets of Linear Systems:

1.6 - Applications of Linear Systems:

1.7 - Linear Independence:

1.8 - Linear Transformations:

1.9 - The Matrix of a Linear Transformation:

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

2.1 - Matrix Operations:

2.2 - The Inverse of a Matrix:

2.3 - Characterizing Invertible Matrices:

2.8 - Subspaces of R^n:

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

3.1 - Determinants:

3.2 - Determinants and Row Operations:

Worksheet, Solutions

Worksheet, Solutions

Helpful Explanations

Equivalent Systems

Numerical Methods - Jacobi and Gauss-Seidel Iteration

Quizzes

Quiz 1, Solutions