1 Systems of Linear Equations
29 practice problems
- 1.1 Systems of linear equations13 problems
- 1.2 Gauss-Jordan elimination16 problems
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Linear Algebra practice problems
300 practice problems, organized by chapter and topic.
A first linear algebra course covering vector geometry, systems of equations, matrices and linear transformations, determinants, eigenvalues, and orthogonality.
Easy, medium and hard problems. Your student profile saves your completed work. Lesson videos are included for selected topics.
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Section 3.1: Span.
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2 Vectors in Rⁿ
47 practice problems
- 2.1 Vectors and basic operations12 problems
- 2.2 Geometry: The dot product21 problems
- 2.3 Lines and planes in R² and R³14 problems
3 Linear Independence, Span, Subspaces
53 practice problems
- 3.1 Span13 problems
- 3.2 Linear independence13 problems
- 3.3 Systems of linear equations revisited13 problems
- 3.4 Subspaces of Rⁿ14 problems
4 Linear Transformations and Matrix Algebra
82 practice problems
- 4.1 Linear transformations14 problems
- 4.2 Operations on matrices10 problems
- 4.3 Matrix multiplication12 problems
- 4.4 Matrix inverses18 problems
- 4.5 Determinants17 problems
- 4.6 Subspaces associated to matrices11 problems
5 Eigenvalues, Eigenvectors, and Diagonalization
27 practice problems
- 5.1 Eigenvalues and eigenvectors15 problems
- 5.2 Diagonalization12 problems
6 Vector Geometry Revisited
41 practice problems
- 6.1 Orthogonality12 problems
- 6.2 Orthogonal projections10 problems
- 6.3 Orthogonal matrices9 problems
- 6.4 The Spectral Theorem10 problems
7 Supplementary Practice
21 practice problems
- 7.1 Cross products, areas, and volumes7 problems
- 7.2 Polynomial vector spaces6 problems
- 7.3 Least squares and normal equations8 problems
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