Linear Algebra Exercises

Do you want to engage your students more when teaching Linear Algebra? Grasple offers a selection of online exercises and openly licensed material to enhance your education.

Open Exercises

All exercises are created by Delft University of Technology and available under a Creative Commons license. A big thanks to TU Delft for sharing these exercises with the rest of the world. Feel free to reuse these exercises in your courses, as long as you make a proper attribution.

Linear Systems I

9Linear System Definition and Properties

26Solving Linear Systems (one solution)

14Solving Linear Systems (general)

Linear Systems II

16Vector Definition and Arithmetic

5Vector Equations

15Linear Combinations and Span

17Matrix Equations

18Solution Set Structure

35Linear Independence

Linear Transformation

21Linear Transformations Definition and Properties

13Standard Matrix

3Linear Transformations One-to-One and Onto

Matrix Algebra

11Addition, Scalar Multiplication and Transposition

31Matrix Operations

3Elementary Matrices

14Inverse matrices (Theory)

20Inverse Matrices (Computing the Inverse)

4Partitioned Matrices

6LU-Factorization

Subspaces

11Subspaces Definition and Properties

3Basis (Theory)

9Finding a Basis

6Coordinates

8Dimension and Rank

Determinants

14Cofactor-Expansion

9Determinants Using Row and Column Operations

15Determinants: Rules of Calculation

5Applications of Determinants - Area and Volume

8Applications of Determinants - Cramer's Rule

Eigenvectors

5Markov Chains

13Definition Eigenvector and Eigenvalue

6Eigenspaces

8The Characteristic Equation

4Similarity

13Diagonalization and Diagonalizability

13Complex Eigenvalues

9Systems of Linear Differential Equations

Orthogonality

10Inner Product

4Orthogonal Projections on a Line

11Orthogonal and Orthonormal Sets

4Orthogonal Projections

4QR Factorization

5The Gram-Schmidt Process

2Least-Squares Method

5Regression

Symmetric Matrices

15Symmetric Matrices: Definitions and Properties

6Orthogonal Diagonalization

15Quadratic Forms

6Constrained Optimization

8Singular Value Decomposition

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Looking for a specific field in mathematics?

As you can see, we have an extensive list of Linear Algebra exercises. But there’s more! Click on the topics below to view more openly licensed practice material, or simply create your own.

Pre-Algebra

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Pre-Algebra

Calculus

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Calculus

Integral Calculus

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Integral Calculus

Statistics

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Statistics

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