1 | Perform the arithmetic operations of matrix addition, and multiplication. |
2 | Use Gaussian elimination or Gauss-Jordan method to find the general solution of a linear system. |
3 | Express an invertible matrix as a product of elementary matrices. |
4 | Find an LU decomposition of a square matrix. |
5 | Use the cofactor expansion to evaluate the determinant of a square matrix. |
6 | Use Cramer’s rule to solve linear systems of equations. |
7 | Perform algebraic operations on vectors: addition, subtraction, and scalar multiplication. |
8 | Determine whether a given set with two operations is a vector space. |
9 | Determine whether a subset of a vector space is a subspace. |
10 | • Determine whether a set of vectors is linearly independent or linearly dependent. |