MAT 141E - Linear Algebra I

Course Objectives

1) Introduce the students to the systems of linear equations and the matrix algebra.
2) to teach the usage of matrices in the interpretation of the solutions of linear systems of equations.
3) To define the determinant function and give some properties of determinants and connect determinants to derivation of an inverse matrix and to the solutions of linear sistems of equations.
4) To give knowledge about vector spaces, subspaces, linear independence, bases and dimension of vector spaces, and coordinates.
5) To introduce inner products in vector spaces and develope orthogonality in a vector space.

Course Description

Systems of linear equations and matrices; matrix algebra, special types of matrices, elementary row and column operations, echelon form, elementary matrices, inverses, equivalent matrices. Determinants; properties of determinants, cofactor and adjoint of a matrix, derivation of inverse matrix, solutions of systems of linear equations, Cramer's rule. Vector Spaces; vector spaces, subspaces, linear independence, bases and dimension, coordinates, change of basis, rank of a matrix. Inner product spaces; standard inner product, orthogonal subspaces, orthogonal complement of a subspace, inner product, inner product spaces, normed space, Cauchy-Schwarz inequality, orthogonal basis, orthogonal matrices, Gram-Schmidt orthogonalization methods.