Linear Algebra - Questions with Solutions
Linear algebra questions with solutions and detailed explanations on matrices , spaces, subspaces and vectors , determinants , systems of linear equations and online linear algebra calculators are included.
Matrices
- Matrices with Examples and Questions with Solutions.
- Transpose of a Matrix.
- Symmetric Matrix.
- Identity Matrix.
- Diagonal Matrices.
- Triangular Matrix.
- Diagonalization of Matrices.
- Inverse Matrix Questions with Solutions.
- Find Matrix Inverse Using Row Operations
- Add, Subtract and Scalar Multiply Matrices.
- Multiplication and Power of Matrices
- Eigenvalues and Eigenvectors Questions with Solutions
- Find Eigenvectors and Eigenvalues of a 3 by 3 Matrix on Video (Video)
- Find Eigenvectors and Eigenvalues of a 2 by 2 Matrix on Video (Video)
- Row Operations and Elementary Matrices.
- The Three Row Operations on Augmented Matrices .
- Write a Matrix in Reduced Row Echelon Form.
- Pivots of a Matrix in Row Echelon Form - Examples with Solutions.
- Null Space and Nullity of a Matrix .
- Column and Row Spaces and Rank of a Matrix .
- Free and Basic Variables of a Matrix - Examples with Solutions.
- Orthogonal Matrices - Examples with Solutions.
- The QR Decomposition of a Matrix.
- LU Decomposition of a Matrix.
- Properties of Matrix Operations .
Least Squares Problems
- Solve Least Squares Problems by the Normal Equations.
- Solve Least Squares Problems by the QR Decomposition.
Spaces, Subspaces and Vectors
- Vector Spaces - Examples with Solutions.
- Subspaces - Examples with Solutions.
- Vectors in ℝn.
- Inner Product, Orthogonality and Length of Vectors .
- Orthogonal Vectors - Examples with Solutions .
- Linear Combinations of Vectors.
- Span of Vectors.
- Linearly Independent and Dependent Vectors - Examples with Solutions .
- Testing for Linearity of Vectors in a Subspace - Examples with Solutions .
- Basis, Coordinates and Dimension of Vector Spaces .
- Change of Basis - Examples with Solutions .
- Orthonormal Basis - Examples with Solutions .
- The Gram Schmidt Process for Orthonormal Basis . Examples with Solutions
determinants
Systems of Linear Equations
- The Three Elementary Operations on Systems.
- Gaussian Elimination to Solve Systems - Questions with Solutions.
- The Elimination Method in Systems - Questions with Solutions.
- Cramer's Rule with Questions and Solutions.
Videos on Linear Algebra
- Find Eigevectors and Eigenvalues of a 2 by 2 Matrix .
- Solve a 2 by 2 System of Equations by Elimination .
- Gaussian Elimination to Solve a 3 by 3 System of Equations .
- Inverse of 3 by 3 Matrix Using Gauss-Jordan .
Linear Algebra Calculators
- Find the Inverse of a Matrix Using Row Reduction .
- Multiply Matrix Calculator .
- Add Matrices Calculator .
- Row Echelon Form Calculator .
- Row Reduce Agmented Matrices - Calculator .
- Online Calculator for The Determinant of a Matrix of Any Size .
- QR Decomposition of Matrices Calculator .
- Online LU Decomposition of a Matrix Calculator.
- Systems of Equations with Complex Coefficients Solver.
- Matrix Calculator Multiplication ; step by step calculator for educational purposes.
