Catalog description: A study of vectors, matrices and linear transformations, principally in two and three dimensions, including treatments of systems of linear equations, determinants, and eigenvalues. Prerequisite: MAT 1120 or permission of the instructor.
Students will
link fundamental structures of linear algebra including systems of linear equations, vectors, matrices, spaces, and linear transformations
connect fundamental linear algebra concepts including determinants and eigenvalues to multiple structures listed above
implement algebraic skills relevant to linear algebra
demonstrate spatial visualization skills in two and three dimensions
employ appropriate software to solve linear algebra problems
investigate applications of linear algebra
communicate linear algebra in written and/or oral forms
interpret statements and identify examples to think critically and creatively about linear algebra
Students will
Apply elementary row operations to transform a matrix into its row echelon form (CLO 3)
Recognize systems of homogeneous linear equations (CLO 3, 4)
Link algebra and geometry of systems of linear equations and their solutions (CLO 3,4)
Determine solutions to systems of linear equations by hand and in Maple. (CLO 3, 4, 5, 7)
Classify linear systems as consistent or inconsistent (CLO 3, 4, 8)
Interpret statements about systems of linear systems and their solutions (CLO 3, 4, 7, 8)
Students will
Compute sums, scalar products, and linear combinations of vectors, and the product of a matrix and a vector (CLO 3, 4)
Characterize linear combinations of vectors and the span of a set of vectors, both algebraically and geometrically (CLO 1, 3, 4)
Determine if a set of vectors is linearly independent (CLO 1, 3, 4) (1.7)
Express infinite solution sets in parametric form (CLO 1, 3, 4)
Link matrix equations, vector equations, and systems of equations (CLO 1, 3, 4)
Apply vectors and systems of equations and their solution sets to real life (CLO 6)
Interpret statements about vectors, systems of equations and their solution sets, and their interplay (CLO 1, 3, 4, 7, 8)
Students will
Determine scalar multiples of matrices (CLO 3, 4, 5)
Determine sums of matrices (CLO 3, 4, 5)
Determine products of matrices (CLO 3, 4, 5)
Determine inverse of matrices (CLO 3, 4, 5)
Determine transpose of matrices (CLO 3, 5)
Connect matrix multiplication to matrix-vector products and row operations (1, 3, 5)
Apply the inverse matrix theorem (CLO 1, 3, 4, 5)
Apply matrix algebra to real life (CLO 6)
Interpret statements about matrix algebra (CLO 1, 3, 4, 7, 8)
Students will
Determine the image of a vector under a linear transformation (CLO 1, 3, 4)
Describe the standard matrix of a linear transformation (CLO 1, 3, 4)
Characterize transformations as linear or nonlinear using the definition. (CLO 1, 3, 4)
Interpret linear transformations in R^2 and R^3 as matrix-vector products. (CLO 1, 3)
Investigate geometric interpretations of linear transformations of the plane and 3-space (CLO 1, 4, 5)
Connect function composition and inverse functions for linear transformations to matrix multiplication and inverse matrices (CLO 1, 3, 4, 5)
Connect kernel and range of linear transformations to uniqueness and existence of solutions to linear systems (CLO 1, 3, 4)
Compute norms and inner products in R^n (CLO 3, 4, 5)
Determine if vectors are orthogonal in R^n (CLO 3, 4, 5)
Apply linear transformations and orthogonality to real life, including computer graphics (CLO 6)
Interpret statements about linear transformations, norms and orthogonality (CLO 1, 3, 4, 7, 8)
Students will
Determine basis and dimension for subspaces of R^n (CLO 3, 4, 5)
Determine whether a given set is a subspace (CLO 1, 3, 4, 5)
Determine coordinates of vectors with respect to a given basis (CLO 1, 3, 4)
Find the coordinates of a vector with respect to a given basis
Apply definitions of null and column spaces of a matrix (CLO 1, 2, 6)
Connect spaces to the invertible matrix theorem (CLO 1, 2, 8)
Apply the rank-nullity theorem (CLO 1, 3, 4, 5)
Interpret statements about spaces (CLO 1, 2, 3, 4, 7, 8)
Interpret a basis as a minimal spanning set and maximal linearly independent set (CLO 1, 2, 3, 4, 8)
Students will
Apply algorithms including cofactor expansion to find determinants (CLO 2, 3, 5)
Investigate geometric interpretations of determinants, including the impact of row operations (CLO 1, 2, 3, 4, 5)
Connect determinants to the invertible matrix theorem (CLO 1, 2, 8)
Determine basis and dimension for subspaces of R^n (CLO 3, 4, 5)
Determine eigenvalues, eigenvectors, and the characteristic polynomial by hand and in Maple. (CLO 2, 3, 4, 5, 7)
Determine bases for eigenspaces. (CLO 1, 2, 3, 4)
Connect the characteristic polynomial to the definition of eigenvalues, linear systems, and determinants. (CLO 1, 2)
Link algebra and geometry of eigenvalues and eigenvectors (CLO 2, 3)
Apply eigenvalues and eigenvectors to real life. (CLO 6)
Characterize the long-term behavior of dynamical systems using eigenvalue decompositions (CLO 1, 2, 3, 4, 6).
Interpret statements about determinants, eigenvalues, eigenvectors, and eigenspaces. (CLO 1, 2, 3, 4, 7, 8)