MAMC.A.2

MAMC.A.2: recognize and apply properties of matrices; find the determinants of 2-by-2 and 3-by-3 matrices; represent a 3-by-3 system of linear equations as a matrix and solve the system in multiple ways the inverse matrix, row operations, and Cramer's Rule; apply properties of similar and orthogonal matrices to prove statements about matrices; find and apply the eigenvectors and eigenvalues of a 3-by-3 matrix; determine if a given set is a vector space; determine whether a vector v is a linear combination of the vectors in S; express a vector in a linearly independent set as a linear combination of the vectors in the set; determine whether a given set of vectors span; determine whether a set of vectors is linearly independent or linearly dependent; show that a set of vectors is a basis for a vector space; find a basis for the null space, row space, and column space of a matrix; find the rank and nullity of a matrix