code BA204 credit_hours 3 title Linear Algebra arbic title prequisites BA102 credit hours 3 Description/Outcomes This course illustrates the nature of mathematics as a blend of technique, theory, and applications. The important problem of solving systems of linear equations leads to the algebra of matrices, determinants, vector spaces, bases and dimension, linear transformations, and Eigen values. Vector spaces are studied in an abstract setting, examining the concepts of linear independence, span, bases, subspaces, and dimension. There follows a discussion of the association between linear transformations and matrices. arabic Description/Outcomes objectives Upon completion of this course, students should be able to:1. Learn the basic theory of linear algebra through Eigen values.2. Realize the wide applicability of linear algebra by examining applications.3. Learn some useful algorithms for linear systems. arabic objectives ref. books David Poole, Linear Algebra: A Modern Introduction, 3rd Edition, Brooks Cole, 2010. arabic ref. books textbook Lay, David C, Linear Algebra and Its Applications with CD/ROM, Update, 3rd Edition. Addison Wesley, 2006. arabic textbook objective set combined content set bullets
Course Content
content serial Description
1 â€¢ Classification of Matrixrnâ€¢ Matrix Algebraic Operations â€¢ Define what is meant by Matrixrnâ€¢ Describe types of matrices and its Algebraic operations â€¢ Examine and Evaluate Algebraic operations of Matrices â€¢ Apply the Eigen values and Eigen vectors in applications such as graph Laplacianrn â€¢ Communicate scientific findings in vector spacern
2 â€¢ Matrix transpose Determinants â€¢ Define The transpose of Matrixrnâ€¢ Define The Matrix Determinants â€¢ Extract Determinants with different order rn
3 rnâ€¢ Matrix inverse â€¢ Describe Matrix Inverse â€¢ Evaluate Matrix Inverse rnâ€¢ Solve square linear system with unique solution using matrix inverse rn
4 â€¢ Equivalent matrices â€“ rank of the matrix â€¢ Define Equivalent Matrices rnâ€¢ Define Matrix Rank â€¢ Examine Equivalent Matrices rnâ€¢ Evaluate Matrix Rankrn
5 â€¢ Equivalent matrices â€“ rank of the matrix â€¢ Define Equivalent Matrices rnâ€¢ Define Matrix Rank â€¢ Examine Equivalent Matrices rnâ€¢ Evaluate Matrix Rankrn
6 rnâ€¢ Consistence of system of linear equations â€¢ Identify consistency of the linear system â€¢ Examine the consistency of the linear system and find its solutionrn
7 â€¢ Vector algebra â€¢ Define Vector rnâ€¢ Discuss Vectors Algebraic Operations â€¢ Solve Algebraic operations about vector addition, scalar multiplication, inner products, projections, norms, orthogonal vectorsrn
8 â€¢ Eigen values and Eigen vectors â€¢ Define Eigen values and Eigen vectors of a given matrix â€¢ Determine the Eigen values and Eigen vectors of a given matrixrn
9 â€¢ Vector space â€¢ Define Vector spacernâ€¢ Describe The characteristics of a Vector Space â€¢ Examine the characteristics of a Vector Space on different problems rnâ€¢ Build a matlab computer program to calculate Gram-Schmidt rnâ€¢ Evaluate numerical stabilityrn rn rn rn rn â€¢ Enlist researchable problemsin the field of linear algebra rnrnrn
10 â€¢ Subspaces â€¢ Define The Subspace of a Vector Space â€¢ Examine the Subspace of given problems
11 rnâ€¢ Linear independence , The span â€¢ Define linear independence Span rnâ€¢ Describe linear independence vectors , Spanning sets â€¢ Solve algebraic problems about linear independence, spanning setsrn
12 â€¢ Basis and Dimension â€¢ Define basis and dimension of a vector space rn â€¢ Determine basis and dimension of abstract vector spaces rn
13 â€¢ Orthonormal basis rnâ€¢ Gram-Schmidt process â€¢ Define Orthonormal basis (A.5)rnâ€¢ Describe Gram-Schmidt process â€¢ Apply Gram-Schmidt process to orthogonalize vectorsrn
14 rnâ€¢ Linear transformationrnâ€¢ Diagonalization â€¢ Define linear mapping rnâ€¢ Describe Matrix diagonalization â€¢ Examine linear mapsrnâ€¢ Apply diagonalization process rn
15 rnGeneral Revisionrn
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