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Expert solutions for matrices, vectors, and transformations

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Linear Algebra Topics

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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 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
Inverse of Matrices
The determinant of a 2 x 2 matrix
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
Determinant of a Matrix
The determinant of a 3 x 3 matrix (General & Shortcut Method)
Properties of determinants
Solving linear systems using Cramer's Rule
video
Eigenvalue and Eigenvectors
Eigenvalues and eigenvectors
The characteristic equation
Diagonalization
Complex eigenvalues
Discrete dynamical systems
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Orthogonality and Least Squares
Inner product, length, and orthogonality
Orthogonal sets
Orthogonal projections
Least-squares problem
Applications to linear models
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