1Perform rigorous proofs using the definitions of vector space, subspace, linear combination of vectors, linear dependence and linear independence, bases and dimension.

2Perform rigorous proofs using the definitions of linear transformation and the null space and range of a linear transformation.

3Exhibit a clear understanding of the relationship between composition of linear transformation and matrix multiplication.

4Understand elementary matrices and their use in describing the solution set of a system of linear equations.

5Understand that the determinant function on n x n matrices with entries in a field F is a function that may be defined recursively, and may be uniquely defined as an alternating multilinear form which takes the identity matrix to

66. Perform rigorous proofs involving eigenvalues and eigenvectors.

7Understand and be able to apply conditions for a linear operator on a finite-dimensional vector space to be diagonalizable.

8Preform calculations with Gram-Schmidt, least squares and related topics.

9Students should be able to do rigorous proofs involving inner product spaces and related topics.