- Degree Bachelor
- Code: BA204
- Credit hrs: 3
- Prequisites: EBA1204
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.
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| content serial | Description |
|---|---|
| 1 | • Classification of Matrixrn• Matrix Algebraic Operations • Define what is meant by Matrixrn• Describe types of matrices and its Algebraic operations • Examine and Evaluate Algebraic operations of Matrices • Apply the Eigen values and Eigen vectors in applications such as graph Laplacianrn • Communicate scientific findings in vector spacern |
| 2 | • Matrix transpose Determinants • Define The transpose of Matrixrn• Define The Matrix Determinants • Extract Determinants with different order rn |
| 3 | rn• Matrix inverse • Describe Matrix Inverse • Evaluate Matrix Inverse rn• Solve square linear system with unique solution using matrix inverse rn |
| 4 | • Equivalent matrices – rank of the matrix • Define Equivalent Matrices rn• Define Matrix Rank • Examine Equivalent Matrices rn• Evaluate Matrix Rankrn |
| 5 | • Equivalent matrices – rank of the matrix • Define Equivalent Matrices rn• Define Matrix Rank • Examine Equivalent Matrices rn• Evaluate Matrix Rankrn |
| 6 | rn• Consistence of system of linear equations • Identify consistency of the linear system • Examine the consistency of the linear system and find its solutionrn |
| 7 | • Vector algebra • Define Vector rn• Discuss Vectors Algebraic Operations • Solve Algebraic operations about vector addition, scalar multiplication, inner products, projections, norms, orthogonal vectorsrn |
| 8 | • Eigen values and Eigen vectors • Define Eigen values and Eigen vectors of a given matrix • Determine the Eigen values and Eigen vectors of a given matrixrn |
| 9 | • Vector space • Define Vector spacern• Describe The characteristics of a Vector Space • Examine the characteristics of a Vector Space on different problems rn• Build a matlab computer program to calculate Gram-Schmidt rn• Evaluate numerical stabilityrn rn rn rn rn • Enlist researchable problemsin the field of linear algebra rnrnrn |
| 10 | • Subspaces • Define The Subspace of a Vector Space • Examine the Subspace of given problems |
| 11 | rn• Linear independence , The span • Define linear independence Span rn• Describe linear independence vectors , Spanning sets • Solve algebraic problems about linear independence, spanning setsrn |
| 12 | • Basis and Dimension • Define basis and dimension of a vector space rn • Determine basis and dimension of abstract vector spaces rn |
| 13 | • Orthonormal basis rn• Gram-Schmidt process • Define Orthonormal basis (A.5)rn• Describe Gram-Schmidt process • Apply Gram-Schmidt process to orthogonalize vectorsrn |
| 14 | rn• Linear transformationrn• Diagonalization • Define linear mapping rn• Describe Matrix diagonalization • Examine linear mapsrn• Apply diagonalization process rn |
| 15 | rnGeneral Revisionrn |
| 16 | |
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