MATH 230 - Linear Algebra

Credits: 4
Lecture Contact Hours: 4
Description: Topics covered in this course include systems of linear equations, matrices, determinants, Euclidean vector spaces, general vector spaces, inner product spaces, eigenvalues and eigenvectors, diagonalization, linear transformations and applications.

Prerequisites: MATH 150 with a minimum grade of 2.0
Corequisites: None.
Recommended: None.

Course Category: Liberal Arts | Mathematics
This course counts toward Schoolcraft’s General Education Requirements.
This course counts toward a Michigan Transfer Agreement General Education Requirement.

This Course is Typically Offered: Fall, Winter
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Course Competencies

Calculate an expression involving matrix operations including addition, subtraction, multiplication, scalar-multiplication, and transposition.
Calculate the determinant of a given matrix using various techniques including cofactor expansion, row reduction, and shortcuts for small or triangular matrices.
Calculate the multiplicative inverse of a given square matrix using various techniques including Gauss-Jordan Elimination and the adjoint-determinant method.
Determine the solution of a system of linear equations using various techniques including Gauss, Gauss-Jordan, matrix-inverse, and Cramer methods.
Calculate an expression involving vector operations, including addition, subtraction, scalar-multiplication, dot-multiplication, cross-multiplication, magnitudes, and parallel and perpendicular projections.
Figure out equations for a line or plane in three-dimensional Euclidean space, given certain facts about the line or plane.
Determine whether a given set of objects and operations constitute a vector space or subspace by using the relevant axioms.
Determine whether a given set of vectors is linearly independent, whether it spans a given vector space, and whether it constitutes a basis for the vector space.
Construct a basis for the null space of a given system of linear equations.
Construct a basis for the linear span of a given set of vectors.
Calculate the coordinates of a given vector relative to a given basis.
Calculate the change-of-basis matrix for transitions from one given basis to another.
Translate the coordinates of a given vector from one basis to another by using the change-of-basis matrix.
Determine whether a given scalar function on a given vector space constitutes an inner product by using the relevant axioms.
Calculate lengths, distances, and angles between vectors using a specified inner product.
Construct an orthonormal basis for a given set of vectors in an inner product space by using the Gram-Schmidt method.
Determine whether a given function between vector spaces constitutes a linear transformation by using the relevant axioms.
Construct a basis for the kernel or for the range of a given linear transformation.
Calculate the matrix that represents a given linear transformation relative to a given pair of bases.
Calculate the values of a given linear transformation (or of its inverse) by using the matrix that represents it.
Determine the eigenvalues and eigenvectors of a given linear transformation or matrix.
Determine a diagonalized or orthogonally diagonalized form for a given linear transformation or matrix.
Calculate powers of a given square matrix by using a diagonalized or orthogonally diagonalized form.
Apply matrix methods to solve selected types of practical problems involving networks, curve-fitting, directed graphs, Markov chains, linear differential equations, conic sections, or quadric surfaces.