
MAT 148  Linear Algebra w/Applications Credits: 4 Lecture Hours: 4 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: General A study of the use and application of matrices in the solution of systems of linear equations, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, bases and projections. Linear algebra is a core course in many engineering, physics, mathematics and computer science programs. This course makes heavy use of computing technology. Graphing calculators required. Prerequisite: MAT 211 with a C or better Competencies
 Solve a system of linear equations
 Identify whether a system of linear equations has none, one or infinitely many solutions
 Solve a system of linear equations using rowreduction and backsubstitution
 Perform arithmetic operations with vectors
 Discuss the span of a set of vectors
 Solve the matrix equation Ax=b
 Decide whether a set of vectors is linearly independent
 Discuss linear transformations from one Euclidean space to another
 Identify whether a transformation is onetoone
 Perform operations on matrices
 Compute a linear combination of matrices
 Computer the product of two matrices, if it exists
 Write the transpose of a matrix
 Find the inverse of a matrix, if it exists
 Perform arithmetic operations on partitioned matrices
 Discuss various Euclidean spaces
 Define what a Euclidean space is
 Find the dimension of a given space
 Define what a subspace is and state conditions for its existence
 Find the column space of a matrix
 Find the row space of a matrix
 Find the nullspace of a matrix
 State the rank of a matrix and relate it to the column and row spaces of the matrix
 Discuss the determinant of a matrix
 Compute the determinant of a matrix by using a cofactor expansion across a row or down a column
 Describe how various row operations on a matrix affect its determinant
 Use Cramer’s rule to solve a system of linear equations
 Use the determinant of a matrix to determine whether a matrix is invertible
 Discuss vector spaces
 State the definition of a vector space
 State the definition of a vector subspace
 Define what is meant by a linear transformation from one vector space to another
 Decide whether a given set of vectors is linearly independent
 Find the coordinate vector in one coordinate system with respect to another coordinate system
 Find a set of vectors which form a basis of a vector space
 State the dimension of a given vector space
 Use the Rank Theorem to relate the rank of a matrix and the dimension of its nullspace
 State several conditions equivalent to a matrix being invertible
 Find the changeofcoordinate matrix from one coordinate system to another
 Discuss the eigenspace of a matrix
 Find the characteristic polynomial of a matrix
 find the eigenvalues, real and complex, of a matrix
 For each eigenvalue of a matrix, find a corresponding eigenvector
 use eigenvalues and eigenvectors to diagonalize a matrix
 Write the Jordan form of a matrix
 Perform vector operations in ndimensional space
 Compute the inner product of two column matrices or, equivalently, the dot product of two vectors
 Calculate the angle between two vectors
 Compute the length (or norm) of a vector
 Decide whether a given set of vectors forms an orthonormal basis of a vector space
 Find the orthogonal projection of one vector onto another
 given a set of linearly independent vectors spanning a vector space, use the GramSchmidt process to find an orthogonal basis for that space
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