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Linear Algebra · Printable PDFs

Linear Algebra Worksheets with Answer Keys

Printable Linear Algebra worksheets, quizzes and chapter tests, each with a full answer key. Every worksheet matches a free lesson on math.wiki. Chapter 1 is free to download. The full Linear Algebra course, lesson by lesson ›

39 worksheets16 quizzes6 tests6 exams39 lesson handouts

1 of 6Vectors in n dimensions

1

Vectors in n dimensions

Free sample

1.1Adding and scaling vectors in n dimensions worksheet7 problemsPreview Handout PDF Answer key

1.2Dot product, length and orthogonality in n dimensions worksheet7 problemsPreview Handout PDF Answer key

1.3Linear combination worksheet7 problemsPreview Handout PDF Answer key

Quiz 1A8 questions, lessons 1.1 to 1.3PDF Answer key

1.4Span worksheet6 problemsPreview Handout PDF Answer key

1.5Linear independence worksheet5 problemsPreview Handout PDF Answer key

Quiz 1B7 questions, lessons 1.4 to 1.5PDF Answer key

1.6Subspaces worksheet6 problemsPreview Handout PDF Answer key

1.7Basis and dimension worksheet6 problemsPreview Handout PDF Answer key

Quiz 1C7 questions, lessons 1.6 to 1.7PDF Answer key

1Chapter 1 test12 questionsPDF Answer key

EXAMLinear Algebra quarter 1 benchmark18 questions, chapter 1PDFExam + Key Answer key

2

Linear systems and row reduction

2.1Writing a system as a matrix equation worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

2.2Augmented matrices and row operations worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 2A8 questions, lessons 2.1 to 2.2PDFQuiz + Key Answer key

2.3Echelon forms and Gaussian elimination worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

2.4Solving a system by row reduction: one, none or infinitely many solutions worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 2B8 questions, lessons 2.3 to 2.4PDFQuiz + Key Answer key

2.5Reduced row echelon form worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

2.6Rank worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

2.7Multiplying a matrix by a vector worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 2C7 questions, lessons 2.5 to 2.7PDFQuiz + Key Answer key

2.8Homogeneous systems and solutions in parametric vector form worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

2.9Linear systems in use: networks, chemical equations, fitting curves worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 2D8 questions, lessons 2.8 to 2.9PDFQuiz + Key Answer key

2Chapter 2 test12 questionsPDFTest + Key Answer key

EXAMLinear Algebra quarter 2 benchmark16 questions, chapter 2PDFExam + Key Answer key

EXAMLinear Algebra midterm exam16 questions, chapters 1 to 2PDFExam + Key Answer key

3

Matrix algebra and linear transformations

3.1Matrix multiplication worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 3A4 questions, lesson 3.1PDFQuiz + Key Answer key

3.2Linear transformation worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

3.3Finding the matrix of a transformation worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

3.4Composing transformations as a matrix product worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 3B7 questions, lessons 3.2 to 3.4PDFQuiz + Key Answer key

3.5The transpose and symmetric matrices worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

3.6Finding an inverse by row reducing A next to I worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

3.7Kernel worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 3C7 questions, lessons 3.5 to 3.7PDFQuiz + Key Answer key

3.8Image worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

3.9Rank and nullity worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

3.10Coordinates in a basis and change of basis worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 3D8 questions, lessons 3.8 to 3.10PDFQuiz + Key Answer key

3Chapter 3 test12 questionsPDFTest + Key Answer key

4

Determinants and invertibility

4.1What the determinant means worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

4.2Determinants by cofactor expansion worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

4.3Properties of determinants: row operations, products, transposes worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 4A8 questions, lessons 4.1 to 4.3PDFQuiz + Key Answer key

4.4When a matrix or transformation can be undone worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

4.5The invertible matrix theorem worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 4B7 questions, lessons 4.4 to 4.5PDFQuiz + Key Answer key

4Chapter 4 test12 questionsPDFTest + Key Answer key

EXAMLinear Algebra quarter 3 benchmark18 questions, chapters 3 to 4PDFExam + Key Answer key

5

Eigenvalues and eigenvectors

5.1The characteristic equation and finding eigenvalues worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

5.2Finding an eigenvector worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

5.3Diagonalization worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 5A8 questions, lessons 5.1 to 5.3PDFQuiz + Key Answer key

5.4Complex eigenvalues and rotation-scaling matrices worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

5.5Matrix powers, dynamical systems and steady states worksheet7 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 5B8 questions, lessons 5.4 to 5.5PDFQuiz + Key Answer key

5Chapter 5 test12 questionsPDFTest + Key Answer key

6

Orthogonality and least squares

6.1Orthogonal bases and projection onto a subspace worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

6.2The Gram-Schmidt process worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

6.3Least squares: the best approximate solution of Ax = b worksheet6 problemsPreview Handout PDFWorksheet + Key Answer key

Quiz 6A7 questions, lessons 6.1 to 6.3PDFQuiz + Key Answer key

6Chapter 6 test12 questionsPDFTest + Key Answer key

EXAMLinear Algebra quarter 4 benchmark18 questions, chapters 5 to 6PDFExam + Key Answer key

EXAMLinear Algebra final exam18 questions, chapters 1 to 6PDFExam + Key Answer key