MTH 230 - Linear Algebra
Topics include systems of linear equations, vectors and matrices, determinants, vector spaces, linear transformations, eigenvectors and eigenvalues, and inner product spaces. Course also offered in Summer.
Prerequisite: MTH 212 with a grade of C or better, or both MTH 211 and MTH 220 with a grade of C or better in each, or permission of instructor.
Course Learning Outcomes
1.Apply standard matrix operations.
2.Formulate the inverse of a square matrix or determine that the inverse does not exist.
3.Identify conditions that are equivalent to a square matrix being invertible.
4.Evaluate determinants of square matrices using cofactor expansion or row reduction.
5.Solve systems of linear equations by a variety of methods which may include any of the following: Gaussian elimination, Gauss-Jordan elimination, using an inverse matrix (if applicable), or Cramer’s rule (if applicable).
6.Prove that a given subset of a vector space is a subspace or demonstrate that it is not.
7.Prove that a given function is a linear transformation or demonstrate that it is not.
8.Classify sets of vectors using terms such as linearly independent, linearly dependent, basis, orthogonal, or orthonormal
9.Calculate the eigenvalues of a square matrix.
10.Construct bases for a variety of subspaces, which may include any of the following: row space of a matrix, column space of a matrix, null space of a matrix, eigenspace of a matrix, kernel of a linear transformation, or range of a linear transformation.
11.Construct an orthonormal basis for an inner product space by using the Gram-Schmidt process.
12.Diagonalize a square matrix or determine that it is not diagonalizable.
Course Offered Fall, Spring