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**MAKE-UP EXAM**

**Exam Date: **June 6, Tuesday at 12:30

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Last Modified : 17.08.2017

**A C T I V I T I E S**

**Semester:** 2016-2017 Summer

**Instructor: **Prof. Dr. Kenan TaÅŸ

**Lecture Hours: **Monday 11:40-13:10

Tuesday 11:40-13:10

Wednesday 11:40-13:10

**Catalogue Description: **Systems of linear equations. Matrices. Algebraic properties of matrix operations. Special types of matrices. Echelon form of a matrix. Solving linear systems by Gauss-Jordan reduction. Finding the inverse of a matrix by row reduction. Equivalent matrices. Determinants. Properties of determinants. Cofactor expansion. Inverse of a matrix (via its determinant). Other applications of determinants (Cramers rule). Vectors in the plane and in 3-space. Vector spaces. Subspaces. Span and linear independence. Basis and dimension. Row space. Null space. Nullity and rank of a matrix. Homogeneos systems. Change of basis. Transition matrices. Orthogonalization. Linear transformations. Kernel and range of a linear transformation.

**Textbook: ** Elementary Linear Algebra with Applications, 9th ed., B. Kolman and D. R. Hill,Pearson, 2008.

**Reference Book:** Elementary Linear Algebra with Supplemental Applications, International Student Version, 10th ed., H. Anton and C. Rorres, Wiley, 2010.

**Evaluation Criteria: **Two midterm examinations (30% each), one final examination (40%)

The Final Exam will be held on Tuesday 22/08/2017 in HA04 at 15:00.

Topics covered are: Solving systems by row reduction, Inner product spaces, orthogonal and orthonormal basis, Gram-Schmidt orthogonalization process, Linear transformation: kernel and range, matrix of a linear transformation.