# Applied Linear Algebra 1st edition

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• Chapter 1: Solving Linear Systems and the Terminology of Vectors and Matrices
• 1.1: Solving Linear Systems, Gaussian elimination, back substitution (4)
• 1.2: Column vectors, addition, scalar multiplication, the two geometric interpretations (9)
• 1.3: Matrices, addition, scalar and matrix multiplication, matrix form of a linear system (11)
• 1.4: Elementary matrices, permutation matrices, LU factorization (7)
• 1.5: Inverses, Gauss-Jordan elimination, transposes, symmetric matrices (3)

• Chapter 2: Vector Spaces, Linear Transformations, and Their Applications
• 2.1: Vector spaces, subspaces, column space and null space of a matrix (4)
• 2.2: Finding the column space and null space, Echelon form, general factorization, pivot and free variables, superposition, rank, efficient solution methods (20)
• 2.3: Linear independence, basis, dimension, coordinates relative to a basis (9)
• 2.4: The four fundamental subspaces (5)
• 2.5: Applications to networks (5)
• 2.6: Linear transformations (7)
• 2.7: Coordinates of vectors and linear transformations relative to bases (14)

• Chapter 3: Orthogonality and Projections
• 3.1: Orthogonal vectors, subspaces, and orthogonal complements (9)
• 3.2: Projection onto a vector (4)
• 3.3: Projections onto subspaces and least squares approximation (4)
• 3.4: Orthogonal bases, orthogonal matrices, Gram-Schmidt (6)
• 3.5: Function spaces, Fourier series, and orthogonal polynomials (4)

• Chapter 4: Determinants and Their Applications
• 4.1: Definition and properties of the determinant (5)
• 4.2: Formulas for the determinant, cofactor expansions (9)
• 4.3: Applications of determinants (6)

• Chapter 5: Diagonalization and Eigenvalues and Eigenvectors
• 5.1: Eigenvalues, eigenvectors, computation examples (6)
• 5.2: Diagonalization of a matrix (4)
• 5.3: Complex numbers and complex eigenvalue problems (4)
• 5.4: The Google page rank algorithm (3)
• 5.5: Differential equations and matrix exponentials (2)
• 5.6: Complex matrices, the spectral theorem, and similarity (4)
• 5.7: Coordinate change under a change of basis (2)

• Chapter 6: Quadratic Forms and the Singular Value Decomposition
• 6.1: Minima, maxima, saddle points, definite and semi-definite quadratic forms (3)
• 6.2: Tests for positive definiteness (5)
• 6.3: Singular value factorization and decomposition (4)

The Applied Linear Algebra question collection contains more than 170 original questions with randomized answers that correspond to any introduction to linear algebra textbook. This collection was created by Bob Muncaster, an associate professor of mathematics at the University of Illinois at Urbana-Champaign and a longtime WebAssign user. Additional resources will be available soon.

## Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

##### Question Availability Color Key
BLACK questions are available now
GRAY questions are under development

Group Quantity Questions
Chapter 1: Solving Linear Systems and the Terminology of Vectors and Matrices
1.1 4 001 002 003 004
1.2 9 001 002 003 004 005 006 007 008 009
1.3 11 001 002 003 004 005 006 007 008 009 010 011
1.4 7 001 002 003 004 005 006 007
1.5 3 001 002 003
Chapter 2: Vector Spaces, Linear Transformations, and Their Applications
2.1 4 001 002 003 004
2.2 20 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020
2.3 9 001 002 003 004 005 006 007 008 009
2.4 5 001 002 003 004 005
2.5 5 001 002 003 004 005
2.6 7 001 002 003 004 005 006 007
2.7 14 001 002 003 004 005 006 007 008 009 010 011 012 013 014
Chapter 3: Orthogonality and Projections
3.1 9 001 002 003 004 005 006 007 008 009
3.2 4 001 002 003 004
3.3 4 001 002 003 004
3.4 6 001 002 003 004 005 006
3.5 4 001 002 003 004
Chapter 4: Determinants and Their Applications
4.1 5 001 002 003 004 005
4.2 9 001 002 003 004 005 006 007 008 009
4.3 6 001 002 003 004 005 006
Chapter 5: Diagonalization and Eigenvalues and Eigenvectors
5.1 6 001 002 003 004 005 006
5.2 4 001 002 003 004
5.3 4 001 002 003 004
5.4 3 001 002 003
5.5 2 001 002
5.6 4 001 002 003 004
5.7 2 001 002
Chapter 6: Quadratic Forms and the Singular Value Decomposition
6.1 3 001 002 003
6.2 5 001 002 003 004 005
6.3 4 001 002 003 004
Total 182