Linear Algebra Step by Step
Vectors and Matrices
Vector Addition
Scalar Multiplication
Dot Product
Vector Magnitude
Matrix Addition
Matrix Transpose
Gaussian Elimination
Gaussian Elimination on a 3x3 System
Row Echelon Form
Reduced Row Echelon Form
Back Substitution
Inconsistent System
Infinite Solutions
Matrix Multiplication
Identity Matrix
Matrix-Vector Product
Matrix Multiplication (2x2)
Matrix Multiplication (2x3 · 3x2)
Matrix Power
Determinants
Determinant of a 2x2 Matrix
Determinant by Cofactor Expansion
Determinant via Row Reduction
Determinant of a Triangular Matrix
Matrix Inverse
Inverse of a 2x2 Matrix (Adjugate Method)
Inverse via Gauss-Jordan Elimination
Solve a System Using the Matrix Inverse
Vector Spaces
Linear Combination
Span Check
Rank from RREF
Linear Independence
Basis Check
Eigenvalues and Eigenvectors
Characteristic Polynomial
Eigenvalues of a 2×2 Matrix
Eigenvectors of a 2×2 Matrix
Diagonalization of a 2×2 Matrix
Repeated Eigenvalue and Defective Matrices
