MATH 230 Matrix Algebra with Applications

• Perform matrix operations, calculate determinants, find inverses for matrices (where possible), and find the transpose of a matrix
• Use elementary row operations to solve systems of linear equations using Gaussian Elimination and Gauss-Jordan reduction methods
• Apply LU decomposition methods to factorize a matrix
• Identify a system of linear equations as independent, inconsistent, or dependent
• Identify properties of Euclidean vector spaces and the effects of linear transformations
• Perform vector operations; use properties of vector operations; and determine vector subspaces, spanning sets, and bases of vector spaces
• Show that a set of vectors forms the basis for a set, and find the dimension of a subspace
• Find inner products and find a basis for a given inner product space
• Use matrices to perform transformations between vector spaces and to identify isomorphisms
• Find the kernel, range, rank, and nullity of a linear transformation
• Find the standard matrix for a given linear transformation and use this matrix to find the image of a given vector
• Use Gram-Schmidt orthogonalization to find orthonormal vectors
• Apply QR decomposition methods to factorize a matrix
• Find real eigenvalues and eigenvectors of a square matrix
• Diagonalize symmetric matrices
• Apply matrix algebra to data fitting and least squares analysis
• Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation