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Linear Algebra - MATH 220

Covers vectors, matrices, systems of equations, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors.

Study Tools

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Study guides

8

7 Eigenvalues and Eigenvectors

A progressive guide to identifying eigenvalues and eigenvectors, computing eigenspaces, comparing algebraic and geometric multiplicities, and determining when a matrix can be diagonalized.
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5 Vector Spaces

A structured guide to vector spaces, subspaces, spans, independence, bases, dimension, and coordinates, with definitions, tests, examples, and a unified problem-solving workflow.
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8 Applications of Linear Algebra

A progressive guide to modeling applied problems with vectors and matrices, solving linear systems, analyzing transformations, and understanding long-term behavior through eigenvalues and eigenvectors.
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2 Matrices and Matrix Operations

A progressive guide to matrix notation, core operations, transposes, inverses, row reduction, and reliable computational methods for solving linear systems.
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3 Systems of Linear Equations

A progressive guide to representing, reducing, solving, classifying, and applying systems of linear equations using matrices, pivots, and rank.
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6 Linear Transformations

A progressive guide to linear transformations, their kernels and images, matrix representations, composition, change of basis, and the rank-nullity theorem.
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1 Vectors and Geometry

A progressive guide to representing vectors, performing vector operations, measuring length and angles, and using vectors to describe lines and planes in two and three dimensions.
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4 Determinants

A progressive guide to computing determinants, tracking row-operation effects, interpreting geometric meaning, testing invertibility, and applying determinants to linear systems.
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Quizzes

8

5 Vector Spaces

A 14-question quiz on abstract vector spaces, subspaces, spans, linear independence, bases, dimension, and coordinates. The questions progress from foundational recognition to applied reasoning and proof-oriented work.
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3 Systems of Linear Equations

A medium-difficulty quiz on representing, reducing, solving, and interpreting systems of linear equations, including pivots, free variables, consistency, rank, and applications.
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7 Eigenvalues and Eigenvectors

A medium-difficulty quiz on eigenvalues, eigenvectors, eigenspaces, algebraic and geometric multiplicity, and diagonalization. Questions progress from direct application to multi-step reasoning and construction.
Quiz · Updated

1 Vectors and Geometry

A medium-difficulty quiz on vectors and geometry, emphasizing component calculations, geometric interpretation, projections, lines, planes, and linear combinations.
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8 Applications of Linear Algebra

A 14-question quiz on modeling, solving, and interpreting applications of linear algebra. The questions progress from foundational applications to integrated reasoning about transformations, systems, eigenvalues, and sensitivity.
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4 Determinants

A medium-difficulty quiz on determinants, emphasizing computation, matrix properties, geometric meaning, cofactors, invertibility, and applications.
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6 Linear Transformations

A medium-level quiz on linear transformations, including linearity, kernels and images, matrix representations, composition, change of basis, and rank-nullity.
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2 Matrices and Matrix Operations

A medium-difficulty quiz on matrix notation, operations, multiplication, transposes, inverses, elimination, and computational methods. Questions progress from foundational interpretation to applied calculation and explanation.
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Flashcards

8

7 Eigenvalues and Eigenvectors

A focused flashcard set covering eigenvalues, eigenvectors, eigenspaces, multiplicities, independence, characteristic polynomials, and matrix diagonalization.
Flashcards · Updated

3 Systems of Linear Equations

A focused flashcard set covering matrix representations, row reduction, pivots, solution types, rank, and applications of systems of linear equations.
Flashcards · Updated

5 Vector Spaces

A focused review of abstract vector spaces, subspaces, spans, independence, bases, dimension, and coordinates.
Flashcards · Updated

1 Vectors and Geometry

A focused study tool covering vector representations, operations, span, norms, dot products, projections, lines, and planes in geometry and multivariable calculus.
Flashcards · Updated

8 Applications of Linear Algebra

A focused set of flashcards on modeling, solving, transforming, and interpreting systems using vectors, matrices, determinants, and eigenvalues.
Flashcards · Updated

6 Linear Transformations

Review the core concepts, matrix representations, compositions, change of basis, and dimension theorems governing linear transformations.
Flashcards · Updated

2 Matrices and Matrix Operations

A focused review of matrix notation, operations, transposes, inverses, row reduction, and numerical solution methods.
Flashcards · Updated

4 Determinants

A focused review of determinant formulas, computation, geometric meaning, cofactors, invertibility, and applications to linear systems.
Flashcards · Updated