How many Linear Algebra practice problems are here?

210, spread across 12 skills — each with a full worked solution.

Are the solutions checked?

Yes. Problems and solutions are generated by SymPy, so every step on the page is algebraically verified rather than written by hand or by a language model.

Course

Linear Algebra — Practice Problems with Worked Solutions

Vectors, matrices, vector spaces, and the transformations behind modern math.. 210 problems across 12 skills, each solved step by step and verified by a computer algebra system.

210
problems: 12
skills: 4
units: 7
formulas

Vectors & Matrices

Vector OperationsCombine vectors and read coordinates with confidence.17 worked problems
Dot ProductsMeasure alignment and build orthogonality intuition.17 worked problems
Matrix ProductsTurn row-by-column multiplication into a reliable reflex.17 worked problems

Systems & Elimination

Linear SystemsSolve Ax=b and verify the result directly.17 worked problems
Row ReductionReduce matrices to expose pivots and solutions.17 worked problems
DeterminantsTrack scaling, orientation, and invertibility.18 worked problems
Matrix InversesReverse an invertible linear action.18 worked problems

Vector Spaces

Linear IndependenceDetect redundant directions using rank.18 worked problems
Rank & BasisCount the independent directions a matrix can reach.18 worked problems
Orthogonal ProjectionsFind the closest point along a direction.18 worked problems

Transformations & Spectrum

Linear TransformationsApply matrix maps and interpret their output.17 worked problems
EigenvaluesFind directions whose scale survives a transformation.18 worked problems

Linear Algebra formula sheets

Vectors and matrices

Other courses

Calculus I
Calculus II
Multivariable Calculus
Differential Equations
Probability & Statistics
Math Foundations