Welcome to Linear Algebra. This course will cover Linear Equations, Matrix Algebra, Determinants, Vector Spaces, Eigenvalues and Eigenvectors, Orthogonality, and more! If you have any suggestions or would like more practice on a certain topic, please send your suggestions to contact@trevtutor.com

### Lectures

##### Linear Equations

Systems of Equations and Matrix Notation

Solving Systems of Equations

Solving Systems of Equations (Practice Questions)

Echelon Forms and Pivots

Solution Sets for Systems of Equations

Adding and Multiplying Vectors

Properties of Vectors

Linear Combinations

Span of Vectors

Matrix Equation Ax=b

Computing Ax and Identity Matrices

Proving Properties of Ax

Homogeneous Linear Systems and Parametric Form

Nonhomogeneous Linear Systems

Linear Independence

Linear Transformations

Matrices and Transformations

Geometric Transformations

Injective and Surjective Transformations

Linear Systems Exam Solutions

##### Matrix Algebra

Adding and Scaling Matrices

Multiplying Matrices

Matrix Transpose and Properties

Inverse Matrices and 2×2 Inverses

Solving Systems with Inverses, and Inverse Identities

Elementary Matrices and Invertibility

##### Vector Spaces

Vector Spaces

Subspaces

Null Space

Column Space

Kernel and Range

Basis and Linear Independence

Spanning Set Theorem

Coordinates and Change-of-Coordinates Matrix

Coordinate Mapping and Polynomials

Dimension

Row Space and Rank Theorem

Change of Basis

##### Determinants

Computing Determinants

Cofactor Expansion

Properties of Determinants

##### Eigenvectors and Eigenvalues

Eigenvalues and Eigenvectors

Eigenspace and Linear Independence

The Characteristic Equation

##### Orthogonality and Least-Squares

### Exercises

##### Vector Spaces

Subspace Proofs

Subspace Proofs 2

Vector Space Linear Mapping Proofs

### Exams and Worksheets

Linear Algebra – Linear Systems Exam

Linear Algebra – Linear Systems Exam Solutions

Linear Algebra – Matrix Algebra Quiz

Linear Algebra – Matrix Algebra Quiz Solutions