1Solve systems of linear equations using concepts such as vector spaces, linear dependence, and Gaussian elimination.

2Understand and test for linear independence, calculate the dimension of vector spaces, and apply the rank-nullity theorem in various contexts.

3Define and apply linear transformations, including matrix multiplication, inverses, LU factorization, and coordinate transformations.

4Compute and understand determinants, including their use in calculating matrix inverses and practical applications such as volume calculations.

5Analyze and compute eigenvectors and eigenvalues, and apply diagonalization techniques.