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Become a Linear Algebra Master

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Learn everything from Linear Algebra, then test your knowledge with 400+ practice questions


01 - Getting started
  • 001 Hi! START HERE Course overview
  • 002 Download the formula sheet.html
  • 002 Linear-Algebra.formulas.pdf
  • 003 Become-a-Linear-Algebra-Master.zip
  • 003 The EVERYTHING download.html

  • 02 - Operations on one matrix
  • 001 Introduction to operations on one matrix
  • 002 Gauss-Jordan-elimination.pdf
  • 002 Linear-systems-in-three-unknowns.pdf
  • 002 Linear-systems-in-two-unknowns.pdf
  • 002 Matrix-dimensions-and-entries.pdf
  • 002 Number-of-solutions-to-a-linear-system.pdf
  • 002 Pivot-entries-and-row-echelon-forms.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Representing-systems-with-matrices.pdf
  • 002 Simple-row-operations.pdf
  • 003 Linear systems in two unknowns.html
  • 003 Linear-systems-in-two-unknowns.pdf
  • 004 Linear systems in two unknowns
  • 005 Linear systems in three unknowns.html
  • 005 Linear-systems-in-three-unknowns.pdf
  • 006 Linear systems in three unknowns
  • 007 Matrix dimensions and entries.html
  • 007 Matrix-dimensions-and-entries.pdf
  • 008 Matrix dimensions and entries
  • 009 Representing systems with matrices.html
  • 009 Representing-systems-with-matrices.pdf
  • 010 Representing systems with matrices
  • 011 Simple row operations.html
  • 011 Simple-row-operations.pdf
  • 012 Simple row operations
  • 013 Pivot entries and row-echelon forms.html
  • 013 Pivot-entries-and-row-echelon-forms.pdf
  • 014 Pivot entries and row-echelon forms
  • 015 Gauss-Jordan elimination.html
  • 015 Gauss-Jordan-elimination.pdf
  • 016 Gauss-Jordan elimination
  • 017 Number of solutions to the linear system.html
  • 017 Number-of-solutions-to-the-linear-system.pdf
  • 018 Number of solutions to the linear system
  • 019 BONUS! Extra practice problems. ).html
  • 019 Workbook.operations-on-one-matrix.pdf
  • 019 Workbook.operations-on-one-matrix.solutions.pdf

  • 03 - Operations on two matrices
  • 001 Introduction to operations on two matrices
  • 002 Identity-matrices.pdf
  • 002 Matrix-addition-and-subtraction.pdf
  • 002 Matrix-multiplication.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Scalar-multiplication.pdf
  • 002 The-elimination-matrix.pdf
  • 002 Zero-matrices.pdf
  • 003 Matrix addition and subtraction.html
  • 003 Matrix-addition-and-subtraction.pdf
  • 004 Matrix addition and subtraction
  • 005 Scalar multiplication.html
  • 005 Scalar-multiplication.pdf
  • 006 Scalar multiplication
  • 007 Zero matrices.html
  • 007 Zero-matrices.pdf
  • 008 Zero matrices
  • 009 Matrix multiplication.html
  • 009 Matrix-multiplication.pdf
  • 010 Matrix multiplication
  • 011 Identity matrices.html
  • 011 Identity-matrices.pdf
  • 012 Identity matrices
  • 013 The elimination matrix.html
  • 013 The-elimination-matrix.pdf
  • 014 The elimination matrix
  • 015 BONUS! Extra practice problems. ).html
  • 015 Workbook.operations-on-two-matrices.pdf
  • 015 Workbook.operations-on-two-matrices.solutions.pdf

  • 04 - Matrices as vectors
  • 001 Introduction to matrices as vectors
  • 002 Basis.pdf
  • 002 Linear-combinations-and-span.pdf
  • 002 Linear-independence-in-three-dimensions.pdf
  • 002 Linear-independence-in-two-dimensions.pdf
  • 002 Linear-subspaces.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Spans-as-subspaces.pdf
  • 002 Unit-vectors-and-basis-vectors.pdf
  • 002 Vectors.pdf
  • 002 Vector-operations.pdf
  • 003 Vectors.html
  • 003 Vectors.pdf
  • 004 Vectors
  • 005 Vector operations.html
  • 005 Vector-operations.pdf
  • 006 Vector operations
  • 007 Unit vectors and basis vectors.html
  • 007 Unit-vectors-and-basis-vectors.pdf
  • 008 Unit vectors and basis vectors
  • 009 Linear combinations and span.html
  • 009 Linear-combinations-and-span.pdf
  • 010 Linear combinations and span
  • 011 Linear independence in two dimensions.html
  • 011 Linear-independence-in-two-dimensions.pdf
  • 012 Linear independence in two dimensions
  • 013 Linear independence in three dimensions.html
  • 013 Linear-independence-in-three-dimensions.pdf
  • 014 Linear independence in three dimensions
  • 015 Linear subspaces.html
  • 015 Linear-subspaces.pdf
  • 016 Linear subspaces
  • 017 Spans as subspaces.html
  • 017 Spans-as-subspaces.pdf
  • 018 Spans as subspaces
  • 019 Basis.html
  • 019 Basis.pdf
  • 020 Basis
  • 021 BONUS! Extra practice problems. ).html
  • 021 Workbook.matrices-as-vectors.pdf
  • 021 Workbook.matrices-as-vectors.solutions.pdf

  • 05 - Dot products and cross products
  • 001 Introduction to dot products and cross products
  • 002 Angle-between-vectors.pdf
  • 002 Cauchy-Schwarz-inequality.pdf
  • 002 Cross-products.pdf
  • 002 Dot-and-cross-products-as-opposite-ideas.pdf
  • 002 Dot-products.pdf
  • 002 Equation-of-a-plane-and-normal-vectors.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Vector-triangle-inequality.pdf
  • 003 Dot products.html
  • 003 Dot-products.pdf
  • 004 Dot products
  • 005 Cauchy-Schwarz inequality.html
  • 005 Cauchy-Schwarz-inequality.pdf
  • 006 Cauchy-Schwarz inequality
  • 007 Vector triangle inequality.html
  • 007 Vector-triangle-inequality.pdf
  • 008 Vector triangle inequality
  • 009 Angle between vectors.html
  • 009 Angle-between-vectors.pdf
  • 010 Angle between vectors
  • 011 Equation of a plane, and normal vectors.html
  • 011 Equation-of-a-plane-and-normal-vectors.pdf
  • 012 Equation of a plane, and normal vectors
  • 013 Cross products.html
  • 013 Cross-products.pdf
  • 014 Cross products
  • 015 Dot and cross products as opposite ideas.html
  • 015 Dot-and-cross-products-as-opposite-ideas.pdf
  • 016 Dot and cross products as opposite ideas
  • 017 BONUS! Extra practice problems. ).html
  • 017 Workbook.dot-products-and-cross-products.pdf
  • 017 Workbook.dot-products-and-cross-products.solutions.pdf

  • 06 - Matrix-vector products
  • 001 Introduction to matrix-vector products
  • 002 Dimensionality-nullity-and-rank.pdf
  • 002 Multiplying-matrices-by-vectors.pdf
  • 002 Null-space-of-a-matrix.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Solving-Ax-b.pdf
  • 002 The-column-space-and-Ax-b.pdf
  • 002 The-null-space-and-Ax-O.pdf
  • 003 Multiplying matrices by vectors.html
  • 003 Multiplying-matrices-by-vectors.pdf
  • 004 Multiplying matrices by vectors
  • 005 The null space and Ax=O.html
  • 005 The-null-space-and-Ax-O.pdf
  • 006 The null space and Ax=O
  • 007 Null space of a matrix.html
  • 007 Null-space-of-a-matrix.pdf
  • 008 Null space of a matrix
  • 009 The column space and Ax=b.html
  • 009 The-column-space-and-Ax-b.pdf
  • 010 The column space and Ax=b
  • 011 Solving Ax=b.html
  • 011 Solving-Ax-b.pdf
  • 012 Solving Ax=b
  • 013 Dimensionality, nullity, and rank.html
  • 013 Dimensionality-nullity-and-rank.pdf
  • 014 Dimensionality, nullity, and rank
  • 015 BONUS! Extra practice problems. ).html
  • 015 Workbook.matrix-vector-products.pdf
  • 015 Workbook.matrix-vector-products.solutions.pdf

  • 07 - Transformations
  • 001 Introduction to transformations
  • 002 Adding-and-scaling-linear-transformations.pdf
  • 002 Compositions-of-linear-transformations.pdf
  • 002 Functions-and-transformations.pdf
  • 002 Linear-transformations-as-matrix-vector-products.pdf
  • 002 Linear-transformations-as-rotations.pdf
  • 002 Preimage-image-and-the-kernel.pdf
  • 002 Projections-as-linear-transformations.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Transformation-matrices-and-the-image-of-the-subset.pdf
  • 003 Functions and transformations.html
  • 003 Functions-and-transformations.pdf
  • 004 Functions and transformations
  • 005 Transformation matrices and the image of the subset.html
  • 005 Transformation-matrices-and-the-image-of-the-subset.pdf
  • 006 Transformation matrices and the image of the subset
  • 007 Preimage, image, and the kernel.html
  • 007 Preimage-image-and-the-kernel.pdf
  • 008 Preimage, image, and the kernel
  • 009 Linear transformations as matrix-vector products.html
  • 009 Linear-transformations-as-matrix-vector-products.pdf
  • 010 Linear transformations as matrix-vector products
  • 011 Linear transformations as rotations.html
  • 011 Linear-transformations-as-rotations.pdf
  • 012 Linear transformations as rotations
  • 013 Adding and scaling linear transformations.html
  • 013 Adding-and-scaling-linear-transformations.pdf
  • 014 Adding and scaling linear transformations
  • 015 Projections as linear transformations.html
  • 015 Projections-as-linear-transformations.pdf
  • 016 Projections as linear transformations
  • 017 Compositions of linear transformations.html
  • 017 Compositions-of-linear-transformations.pdf
  • 018 Compositions of linear transformations
  • 019 BONUS! Extra practice problems. ).html
  • 019 Workbook.transformations.pdf
  • 019 Workbook.transformations.solutions.pdf

  • 08 - Inverses
  • 001 Introduction to inverses
  • 002 Inverse-of-a-transformation.pdf
  • 002 Inverse-transformations-are-linear.pdf
  • 002 Invertibility-from-the-matrix-vector-product.pdf
  • 002 Matrix-inverses-and-invertible-and-singular-matrices.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Solving-systems-with-inverse-matrices.pdf
  • 003 Inverse of a transformation.html
  • 003 Inverse-of-a-transformation.pdf
  • 004 Inverse of a transformation
  • 005 Invertibility from the matrix-vector product.html
  • 005 Invertibility-from-the-matrix-vector-product.pdf
  • 006 Invertibility from the matrix-vector product
  • 007 Inverse transformations are linear.html
  • 007 Inverse-transformations-are-linear.pdf
  • 008 Inverse transformations are linear
  • 009 Matrix inverses, and invertible and singular matrices.html
  • 009 Matrix-inverses-and-invertible-and-singular-matrices.pdf
  • 010 Matrix inverses, and invertible and singular matrices
  • 011 Solving systems with inverse matrices.html
  • 011 Solving-systems-with-inverse-matrices.pdf
  • 012 Solving systems with inverse matrices
  • 013 BONUS! Extra practice problems. ).html
  • 013 Workbook.inverses.pdf
  • 013 Workbook.inverses.solutions.pdf

  • 09 - Determinants
  • 001 Introduction to determinants
  • 002 Cramers-rule-for-solving-systems.pdf
  • 002 Determinants.pdf
  • 002 Modifying-determinants.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Upper-and-lower-triangular-matrices.pdf
  • 002 Using-determinants-to-find-area.pdf
  • 003 Determinants.html
  • 003 Determinants.pdf
  • 004 Determinants
  • 005 Cramers rule for solving systems.html
  • 005 Cramers-rule-for-solving-systems.pdf
  • 006 Cramers rule for solving systems
  • 007 Modifying determinants.html
  • 007 Modifying-determinants.pdf
  • 008 Modifying determinants
  • 009 Upper and lower triangular matrices.html
  • 009 Upper-and-lower-triangular-matrices.pdf
  • 010 Upper and lower triangular matrices
  • 011 Using determinants to find area.html
  • 011 Using-determinants-to-find-area.pdf
  • 012 Using determinants to find area
  • 013 BONUS! Extra practice problems. ).html
  • 013 Workbook.determinants.pdf
  • 013 Workbook.determinants.solutions.pdf

  • 10 - Transposes
  • 001 Introduction to transposes
  • 002 Null-and-column-spaces-of-the-transpose.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 The-product-of-a-matrix-and-its-transpose.pdf
  • 002 Transposes-and-their-determinants.pdf
  • 002 Transposes-of-products-sums-and-inverses.pdf
  • 003 Transposes and their determinants.html
  • 003 Transposes-and-their-determinants.pdf
  • 004 Transposes and their determinants
  • 005 Transposes of products, sums, and inverses.html
  • 005 Transposes-of-products-sums-and-inverses.pdf
  • 006 Transposes of products, sums, and inverses
  • 007 Null and column spaces of the transpose.html
  • 007 Null-and-column-spaces-of-the-transpose.pdf
  • 008 Null and column spaces of the transpose
  • 009 The product of a matrix and its transpose.html
  • 009 The-product-of-a-matrix-and-its-transpose.pdf
  • 010 The product of a matrix and its transpose
  • 011 BONUS! Extra practice problems. ).html
  • 011 Workbook.transposes.pdf
  • 011 Workbook.transposes.solutions.pdf

  • 11 - Orthogonality and change of basis
  • 001 Introduction to orthogonality and change of basis
  • 002 Coordinates-in-a-new-basis.pdf
  • 002 Least-squares-solution.pdf
  • 002 Orthogonal-complements.pdf
  • 002 Orthogonal-complements-of-the-fundamental-subspaces.pdf
  • 002 Projection-onto-the-subspace.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 002 Transformation-matrix-for-a-basis.pdf
  • 003 Orthogonal complements.html
  • 003 Orthogonal-complements.pdf
  • 004 Orthogonal complements
  • 005 Orthogonal complements of the fundamental subspaces.html
  • 005 Orthogonal-complements-of-the-fundamental-subspaces.pdf
  • 006 Orthogonal complements of the fundamental subspaces
  • 007 Projection onto the subspace.html
  • 007 Projection-onto-the-subspace.pdf
  • 008 Projection onto the subspace
  • 009 Least squares solution.html
  • 009 Least-squares-solution.pdf
  • 010 Least squares solution
  • 011 Coordinates in a new basis.html
  • 011 Coordinates-in-a-new-basis.pdf
  • 012 Coordinates in a new basis
  • 012 Coordinates-in-a-new-basis.pdf
  • 013 Transformation matrix for a basis.html
  • 013 Transformation-matrix-for-a-basis.pdf
  • 014 Transformation matrix for a basis
  • 015 BONUS! Extra practice problems. ).html
  • 015 Workbook.orthogonality-and-change-of-basis.pdf
  • 015 Workbook.orthogonality-and-change-of-basis.solutions.pdf

  • 12 - Orthonormal bases and Gram-Schmidt
  • 001 Introduction to orthonormal bases and Gram-Schmidt
  • 002 Gram-Schmidt-process-for-change-of-basis.pdf
  • 002 Orthonormal-bases.pdf
  • 002 Projection-onto-an-orthonormal-basis.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 003 Orthonormal bases.html
  • 003 Orthonormal-bases.pdf
  • 004 Orthonormal bases
  • 005 Projection onto an orthonormal basis.html
  • 005 Projection-onto-an-orthonormal-basis.pdf
  • 006 Projection onto an orthonormal basis
  • 007 Gram-Schmidt process for change of basis.html
  • 007 Gram-Schmidt-process-for-change-of-basis.pdf
  • 008 Gram-Schmidt process for change of basis
  • 009 BONUS! Extra practice problems. ).html
  • 009 Workbook.orthonormal-bases-and-gram-schmidt.pdf
  • 009 Workbook.orthonormal-bases-and-gram-schmidt.solutions.pdf

  • 13 - Eigenvalues and Eigenvectors
  • 001 Introduction to Eigenvalues and Eigenvectors
  • 002 Eigenvalues-eigenvectors-eigenspaces.pdf
  • 002 Eigen-in-three-dimensions.pdf
  • 002 RESOURCE Quiz solutions for this section.html
  • 003 Eigenvalues, eigenvectors, eigenspaces.html
  • 003 Eigenvalues-eigenvectors-eigenspaces.pdf
  • 004 Eigenvalues, eigenvectors, eigenspaces
  • 005 Eigen in three dimensions.html
  • 005 Eigen-in-three-dimensions.pdf
  • 006 Eigen in three dimensions
  • 007 BONUS! Extra practice problems. ).html
  • 007 Workbook.eigenvalues-and-eigenvectors.pdf
  • 007 Workbook.eigenvalues-and-eigenvectors.solutions.pdf

  • 14 - Final exam and wrap-up
  • 001 Linear-Algebra.Final-Exam.Practice-1.pdf
  • 001 Linear-Algebra.Final-Exam.Solutions.Practice-1.pdf
  • 001 Practice final exam #1 (optional).html
  • 002 Linear-Algebra.Final-Exam.Practice-2.pdf
  • 002 Linear-Algebra.Final-Exam.Solutions.Practice-2.pdf
  • 002 Practice final exam #2 (optional).html
  • 003 Linear Algebra final exam.html
  • 003 Linear-Algebra.Final-Exam.Solutions.pdf
  • 003 Linear-Algebra.Final-Exam.pdf
  • 004 Wrap-up
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    تاریخ انتشار: 28 دی 1401
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