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

4.1 - Vector Spaces:

4.2 - Column and Null Spaces:

4.3 - Bases:

4.4 - Coordinates:

4.5 - Dimension and Rank:

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

5.1 - Eigenvalues:

5.2 - Eigenvalues and Where to Find Them:

5.3 - Diagonalization:

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

6.1 - Inner Products, Length, and Orthogonality:

6.2 - Orthogonal Sets:

6.3 - Orthogonal Projection:

6.4 - The Gram-Schmidt Process:

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Worksheet, Solutions

Helpful Explanations

Equivalent Systems

Section Notes

Solving Linear Systems

Span and Linear Independence

Matrix Multiplication and Inversion

Basis, Dimension, Null Space, Range Example



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