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Solving A System of Linear Equations Using Row Operations

Solving A System of Equations Using a TI-84

Network Analysis

Kirchhoff's Laws

Adding and Subtracting Matrices

Scalar Multiplication and Matrix Multiplication

Determining Whether A Matrix Product is Defined

The Trace of a Square Matrix

The Transpose of a Matrix

Properties of the Transpose of a Matrix

Finding an Inverse Matrix Using Row Operations

Finding an Inverse of a 2 x 2 Matrix Using a Formula

Solving a 3 x 3 System of Equations Using the Inverse

Elementary Matrices- The Basics

Finding A Sequence of Elementary Matrices

Solve a System of Linear Equations Using LU Decomposition

Finding the Determinant of a 2 x 2 Matrix

Finding the Minors and Cofactors of a 3 x 3 Matrix

Finding the Determinant of a 3 x 3 Matrix Using Minors and Cofactors

Finding the Determinant of a 3 x 3 Matrix (alternative method)

Determinant of a Triangular Matrix

Matrix Conditions Resulting in a Zero Determinant

Properties of Determinants: det(AB) = det(A)det(B)

Linear Algebra- Properties of Determinants (part 2)

Properties of Determinants (part 3)

Introduction to Eigenvalues and Eigenvectors

Use the Characteristic Equation to Find Eigenvalues and Eignevectors

The Adjoint of a Matrix

Cramer's Rule

Using Determinants to Find the Equation of a Line

Introduction to Vectors in the Plane

Properties of Vector Addition and Scalar Multiplication

Vectors in n-space

Writing a Vector as a Linear Combination of Other Vectors

Vector Spaces

Vector Subspaces

Finding the Length of a Vector in R^n/ Finding a Unit Vector

Finding the Angle between Two Vectors

Linear Combinations

Finding Orthogonal Vectors

Determining Whether S is a Basis for an Indicated Vector Space

Finding Bases for Row and Column Spaces

Finding a Basis and Dimension for a Homogeneous System of Linear Equations

Change of Basis in R^n

Finding the Least Squares Solution to a System

The Gram-Schmidt Orthonormalization Process

Determining Whether a Set of Vectors is Orthogonal, Orthonormal, or Neither

Introducing Linear Transformations