Student Learning Outcomes

• Students can solve problems pertaining to the definitions of linear transformation, kernel, and range. The following items were examined: Do students know the definition of the kernel to a linear transformation? Given such a transformation can students correctly encode the transformation into a coefficient matrix? Can students effectively transform the matrix via row operations into a reduced matrix and properly decode the reduced matrix into an appropriate subspace description of the kernel? Score of 0) No attempt, 1) approach recognizes the definition of the kernel, 2) approach correctly applies appropriate row reduction, 3) student obtains the correct number of free variables and correctly constructs a viable representation of the kernel subspace, and 4) the student completes the problem perfectly with only minor computational errors and no conceptual mistakes. Success: At least 70% of students will score above a two
• Students can solve problems pertaining to eigenvalues and eigenvectors.