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# MAT 143 - Lineer Algebra

## Course Objectives

1. To teach matrix algebra and system of linear equations.
2. To teach how to solve a system of linear equations.
3. To teach invertible matrices and the properties of the determinant.
4. To teach vector spaces, subspaces, span of a set, linear independence, basis, coordinates of a vector, and the dimension.
5. To teach the concept of inner product, inner product space and diagonalization methods.
6. To teach linear transformations and their matrix representations.

## Course Description

Linear Equations and Matrices; Systems of linear equations, Matrices, Matrix algebra, Special types of matrices,
Solving Linear Systems; Echelon form a matrix, Solutions of systems of linear equations, Elementary matrices, Inverse of a matrix.
Determinants; Definition, Properties of determinants, Cofactor and adjoint of a matrix, derivation of inverse matrix. Cramer's rule.
Real Vector Spaces; Definition of vector spaces, Subspaces, Linear independence, Bases and dimension, Coordinates, Change of basis and rank of a matrix.
Inner Product Spaces; Standard inner product, Orthogonal subspaces, Orthogonal complement of a subspace, Inner product spaces, Cauchy-Schwarz inequality, Orthogonal basis, Gram-Schmidt method.
Linear Transformations and Matrices; Definition of a linear transformations, The kernel and range of a linear transformation, Matrix representations of a linear transformations.

 Course Coordinator Nurettin Cenk Turgay Course Language Turkish