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Linear Equations with Matrices

Notation of matrices

Solving systems of linear equations by graphing

Representing linear system as a matrix

The three types of matrix row operations

Solving a linear system with matrices using Gaussian elimination

Row reduction and echelon forms

Linear combination and vector equations in \(R^n\)

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The determinant of a 3 x 3 matrix (General & Shortcut Method)

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Inverse of Matrices

2 x 2 invertible matrix

The inverse of a 2 x 2 matrix

Solving linear systems using 2 x 2 inverse matrices

The inverse of a 3 x 3 matrices with matrix row operations

The invertible matrix theorem

Subspace of \(\Bbb{R}^n\)

Properties of subspace

Column space

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Dimension and rank

Eigenvalue and Eigenvectors

Eigenvalues and eigenvectors

The characteristic equation

Diagonalization

Complex eigenvalues

Discrete dynamical systems

Orthogonality and Least Squares

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