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From vectors and matrices to university linear algebra and practical applications.

Shared foundations16 concepts
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FOUNDATIONS · UNIVERSITY · APPLIED LINEAR ALGEBRA

Choose a goal. Check prerequisites. Find your next step.

Build foundations in vectors, systems, bases, dimension, and solution spaces.

Shared skills & course scope

16 concepts, 240 graded exercises, plus diagnostic, repair and transfer probes. Each concept includes calculation, conceptual interpretation or applications. In the university path, deselect units outside your syllabus.

Vectors and linear combinations

Foundation practice
Prerequisites: Basic algebra

Matrices and operations

Foundation practice
Prerequisites: Vectors and linear combinations

Linear systems

Foundation practice
Prerequisites: Matrices and operations

Elimination and echelon form

Foundation practice
Prerequisites: Linear systems

Span and independence

Foundation practice
Prerequisites: Vectors and linear combinations · Elimination and echelon form

Vector subspaces

Foundation practice
Prerequisites: Span and independence

Bases, dimension, and coordinates

Foundation practice
Prerequisites: Vector subspaces · Span and independence

This question bank covers foundations and representative applications, not an entire university course. Mastery reflects independent evidence within this bank; recognizing an argument does not replace writing a proof.

Go deeper: course & learning resources

Questions and mini-lessons here are original. These links provide courses, a textbook and geometric intuition for further study.