Upon completion of this course, students will be able to: solve systems of linear equations and perform operations on vectors; determine if a given set of vectors is linearly independent and perform linear transformations; determine if the inverse of a matrix exists, calculate the inverse of a matrix, and identify geometric changes of matrices; determine if a vector is in a vector space, identify properties of determinants, and apply Cramer’s rule to solve linear systems; determine whether a given set is a vector space or subspace, find a basis for a column space, and map a vector to its coordinate vector in a basis; find the dimension of a subspace, apply the rank theorem, and map a coordinate vector from one base to another; calculate eigenvalues, determine if a vector is an eigenvector, and diagonalize matrices; determine orthogonality projections and orthogonality of vectors; determine symmetry and orthogonality of matrices, find the matrix of a quadratic form; and find the singular values of a matrix.