MATH 207: Matrices and Linear Algebra
(3-0) Cr. 3. F.S.SS.
Prereq: 2 semesters of calculus
Systems of linear equations, determinants, vector spaces, linear transformations, orthogonality, least-squares methods, eigenvalues and eigenvectors. Emphasis on applications and techniques. Only one of MATH 207 and MATH 317 may be counted toward graduation.
Linear Algebra, 5th Edition
Chapter and Section references are to Lay, Linear Algebra 5th ed.
Times are suggested based on a 15-week semester of 44 class meetings, allowing for three unit exams, and two weeks worth of classes for review and exams.
- Chapter 1 and 2 (5 weeks)
- Sec 1.1-1.9 and 2.1-2.6
- Chapter 3 and 4 (3 weeks)
- Sec 3.1-3.3 and 4.1-4.7
- Chapter 5 and 6 (4 weeks)
- Sec 5.1-5.5 and 6.1-6.6
- Chapter 7 (1 week)
- Sec 7.1 and 7.2 and 7.4
Systems of Linear Equations
- Recognize and set up a system of linear equations
- Perform row operations on a system of linear equations to obtain echelon and reduced echelon forms
- Interpret echelon forms to determine solution sets of systems of linear equations
- Apply systems of linear equations to problems in networking, balancing chemical equations, and other areas
Matrix Algebra and Determinants
- Perform matrix arithmetic operations
- Use determinants do determine if a matrix is invertible
- Use determinants to find the inverse of a matrix if it exists
- Apply augmented matrices to find the inverse of a matrix if it exists
- Identify subspaces of n-dimensional real space
- Identify subspaces of abstract vector spaces
- Produce a basis for a given vector space
- Verify if a given set is linearly independent, spanning, or both
- Identity the standard subspaces NulA, ColA, and RowA for a given matrix A
- Give the standard matrix for a given linear transformation
- Interpret matrix multiplication as a composition of linear transformations
- Find change of base matrices and their relationship to a linear transformation
- Relate one-to-one and onto with NulA and ColA and invertibility
Eigenvalues and Eigenvectors
- Understand the definition of eigenvalues and eigenvectors
- Verify if given scalars are eigenvalues
- Use the characteristic polynomial to find all eigenvalues and eigenvectors
- Use the number of eigenvectors to determine if a matrix is diagonalizable
Inner Product Spaces
- Understand orthogonality and magnitude in n-dimensional space
- Utilize inner products in abstract vector spaces
- Use an inner product to induce a norm
- Understand the Gram-Schmidt orthonormalization algorithm, and its relation to the QR-factorization
- Utilize matrices to solve least squares problems
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