MATH312

Perform elementary row operations on matrices; determine and analyze solutions of a system of linear equations.

Perform matrix arithmetic, calculate determinants, and determine inverses to given matrices.

Identify Euclidean spaces and subspaces and other vector spaces.

Identify spans and spanning sets.

Distinguish between linearly dependent and linearly independent sets of vectors.

Identify bases and dimensions of vector spaces.

Calculate characteristic polynomials, eigenvalues and eigenvectors, and diagonalize matrices.

Identify and calculate with orthogonal vectors, orthogonal bases, and orthonormal bases.

Orthogonally diagonalize symmetric matrices.