Course coordinator

Eli Stines

Catalog description

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, 6th Edition
ISBN: 9780136880929


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

Vector Spaces

  • 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

Linear Transformations

  • 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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Students with disabilities

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