MATH2: LINEAR ALGEBRA
A standard one semester Linear Algebra course covering systems of linear equations, vectors and matrices, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors. Graphing calculators and computers will be used. (C-ID: MATH 250) PREREQUISITE: Mathematics 1C with a grade of 'C' or better.
- Students will be able to define and apply Gaussian elimination method for solving the systems of linear equations.
- Define a homogenous linear system of m equations with n unknowns and identify a sufficient condition for its nontrivial solution.
- Students will be able to add and multiply matrices and analyze the properties of Matrix multiplication.
- Students will evaluate the determinants of matrices and will apply the Cramer's rule to solve linear systems.
- Students will be able to compute the transpose, determinant, and inverse of matrices for a given matrix and prove basic theorems relating to deteminants and matrices.
- Students will be able to define subspaces in R-2 and R-3 and inner products; determine the dimension of a subspace and analyze the function that maps two vectors from a vector space to a scalar and prove basic theorems about properties of subspaces.
- Students will differentiate between linearly dependent and linearly independent sets of vectors and will be able to find a basis of the subspace; construct orthogonal and orthonormal bases using the Gram-Schmidt Process for a given basis.
- Demonstrate the knowledge of constructing the orthogonal diagonalization of a symmetric matrix.
- Demonstrate the knowledge of definitions of eigenvalues and eigenvectors and at least of one method to calculate eigenvalues, eigenvectors, and eigenspaces for both matrices and linear transformations.
- Students will be able to define linear transformation, transformations from R to R, matrix transformations, one-to-one, kernel, range, rank, nulity and isomotphism, and to solve application problems using the properties of linear mappings: image and kernel.