Course Information

Course Name	Turkish	Lineer Cebir
	English	Linear Algebra
Course Code	MAT 143	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	1	4	4	-	-
Course Language		Turkish
Course Coordinator		Güler Arsan
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 Outcomes		Students completing this course will be able to: I. Can solve linear equations by using matrix methods. II. Learn and apply the properties of determinants. III. Understand and use real vector spaces and subspaces. IV. Understand basis, dimension and linear independence. V. Learn the concept of inner product inner product space and orthogonalization methods. VI. Learn the concept of linear transformations and their matrix representations.
Pre-requisite(s)
Required Facilities
Other
Textbook		Bernard Kolman, David R. Hill, 2008, “Elementary Linear Algebra with Applications”, 9th Edition, Prentice Hall, ISBN:0-13-135063-3.
Other References		1. Leon, Steven J., 2006, “Linear Algebra with Applications”, 7th Edition Prentice Hall, ISBN: 0- 13-200306-6. 2.Howard Anton, Chris Rorres, 2005, “Elementary Linear Algera”, John Wiley and Sons.

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