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Linear Algebra Topics

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video
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 RnR^nRn
Matrix equation Ax=b
Solution sets of linear systems
Application of linear systems
video
Linear Transformation
Linear independence
Image and range of linear transformations
Properties of linear transformation
The matrix of a linear transformation
video
Matrix Operations
Adding and subtracting matrices
Multiplying a matrix by a scalar
Multiplying a matrix by another matrix
Zero matrix
Identity matrix
Properties of matrix addition
Properties of matrix scalar multiplication
Properties of matrix to matrix multiplication
video
Determinant of a Matrix
The determinant of a 2 x 2 matrix
The determinant of a 3 x 3 matrix (General & Shortcut Method)
Properties of determinants
Solving linear systems using Cramer's Rule
video
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
video
Subspace of \(\Bbb{R}^n\)
Properties of subspace
Column space
Null space
Dimension and rank
video
Eigenvalue and Eigenvectors
Eigenvalues and eigenvectors
The characteristic equation
Diagonalization
Complex eigenvalues
Discrete dynamical systems
video
Orthogonality and Least Squares
Inner product, length, and orthogonality
Orthogonal sets
Orthogonal projections
Least-squares problem
Applications to linear models

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