MATH 272 - Linear Algebra

1. Perform elementary row operations on a matrix to put it in row-echelon or reduced row-echelon form. [REASON]
2. Apply the row reduction of an augmented matrix to solve systems of linear equations, as well as the equivalent vector and matrix forms for those systems. [REASON]
3. Express the solution set of a nonhomogeneous system of linear equations in terms of a particular solution and the solution set of the corresponding homogeneous system. [REASON]
4. Find the standard matrix of a linear transformation. [REASON]
5. Perform the matrix operations of addition, scalar multiplication, and matrix multiplication. [REASON]
6. Determine whether a given matrix is invertible. [REASON]
7. Compute the inverse of a given nonsingular matrix. [REASON]
8. Determine the dimension of and find a basis for a subspace of n-dimensional real space, given a spanning set. [REASON]
9. Compute the determinant of a square matrix using row or column expansion. [REASON]
10. Compute the determinant of a square matrix using properties of the determinant. [REASON]
11. Apply Cramer’s rule to solve a system of linear equations. [REASON]
12. Find bases for the null space and column space of a matrix, and for the kernel and range of a linear transformation. [REASON]
13. Find coordinates of a vector with respect to a given basis. [REASON]
14. Change the basis for a linear transformation. [REASON]
15. Compute eigenvalues and eigenvectors for a matrix or linear transformation. [REASON]
16. Diagonalize a transformation with distinct eigenvalues. [REASON]
17. Use definitions and theorems to justify statements regarding any of the above concepts. [REASON]