Students should be able to solve systems of linear equations, calculate determinants, test for a subspace, show whether a set of vectors is a basis, find its dimension, find a basis, rank and nullity for any fundamental matrix spaces, use the Gram- Schmidt process to find an orthonormal basis, find the eigenvalues, corresponding eigenvectors and determine whether the matrix is diagonalizable. Some applications of linear algebra to engineering are discussed.

Basic of complex numbers