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 from Professor Ponce

Solving Linear Systems

Span and Linear Independence

Matrix Multiplication and Inversion

Basis, Dimension, Null Space, Range Example

Eigenvalues, Eigenvectors, and Diagonalization



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