
20242025 College Catalog

MAT 252  Introduction to Linear Algebra 3 Credits, 3 Contact Hours 3 lecture periods 0 lab periods Introduction to vector spaces and linear transformations. Includes systems of linear equations, vector spaces, inner product spaces, matrices, and linear transformations.
Prerequisite(s): MAT 231 GenEd: Meets AGEC  MATH; Meets CTE  M&S.
Course Learning Outcomes
 Perform operations with matrices, calculate determinants, find eigenvalues and eigenvectors, and use matrices to solve systems of linear equations.
 Define vector spaces and find a basis for a subspace.
 Determine the matrix of a linear transformation with respect to a given basis, its kernel and range, and perform operations with linear transformations.
Performance Objectives:
 Use matrices to solve systems of linear equations; perform operations with matrices, calculate the inverse of a nonsingular matrix, and calculate the determinant of a square matrix.
 Define a vector space and perform vector operations; determine linear independence and find a spanning set of vectors.
 Define subspaces of a vector space; find a basis for a subspace and determine its dimension; find the subspaces associated with a matrix, and determine the rank and nullity of a matrix.
 Define a linear transformation and find the matrix associated with it; determine the kernel and range of a transformation; find the inverse of a transformation and the composition of two or more linear transformations; calculate the change of basis matrix.
 Find the eigenvalues and eigenvectors of a matrix; determine similarity between two matrices; diagonalize a matrix.
 Use the GramSchmidt process to obtain an orthogonal and an orthonormal basis; define an inner product space.
 Use Linear Algebra in various scientific and mathematical applications.
Outline:
 Matrices and Systems of Linear Equations
 Gaussian and GaussJordan elimination
 Matrix operations
 Inverse and determinant of square matrices
 Applications
 Vector Spaces
 Definition
 Algebra of vectors
 Linear independence
 Spanning sets of vectors
 Subspaces
 Definition
 Basis and dimension
 Subspaces associated with a matrix
 Rank and nullity of a matrix
 Linear Transformations
 Definition
 Kernel and range
 Matrix of a linear transformation
 Composition and inverses of linear transformations
 Change of Basis
 Applications
 Eigenvalues and Eigenvectors
 Definition
 Similar matrices
 Diagonalization of matrices
 Orthogonality and Inner Product Spaces
 Orthogonal and orthonormal basis
 Orthogonal projections
 GramSchmidt process
 Orthogonal diagonalization of symmetric matrices
 Applications
 Definition of inner product spaces
 Applications
 Matrices and systems of linear equations
 Linear transformations
 Orthogonality and inner product spaces
Effective Term: Fall 2015

