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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

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â€¢ Matrix transpose Determinants â€¢ Define The transpose of Matrixrnâ€¢ Define The Matrix Determinants â€¢ Extract Determinants with different order rn

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rnâ€¢ Matrix inverse â€¢ Describe Matrix Inverse â€¢ Evaluate Matrix Inverse rnâ€¢ Solve square linear system with unique solution using matrix inverse rn

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â€¢ Equivalent matrices â€“ rank of the matrix â€¢ Define Equivalent Matrices rnâ€¢ Define Matrix Rank â€¢ Examine Equivalent Matrices rnâ€¢ Evaluate Matrix Rankrn

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â€¢ Equivalent matrices â€“ rank of the matrix â€¢ Define Equivalent Matrices rnâ€¢ Define Matrix Rank â€¢ Examine Equivalent Matrices rnâ€¢ Evaluate Matrix Rankrn

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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

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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

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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

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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 GramSchmidt rnâ€¢ Evaluate numerical stabilityrn rn rn rn rn â€¢ Enlist researchable problemsin the field of linear algebra rnrnrn

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â€¢ Subspaces â€¢ Define The Subspace of a Vector Space â€¢ Examine the Subspace of given problems

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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

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â€¢ Basis and Dimension â€¢ Define basis and dimension of a vector space rn â€¢ Determine basis and dimension of abstract vector spaces rn

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â€¢ Orthonormal basis rnâ€¢ GramSchmidt process â€¢ Define Orthonormal basis (A.5)rnâ€¢ Describe GramSchmidt process â€¢ Apply GramSchmidt process to orthogonalize vectorsrn

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rnâ€¢ Linear transformationrnâ€¢ Diagonalization â€¢ Define linear mapping rnâ€¢ Describe Matrix diagonalization â€¢ Examine linear mapsrnâ€¢ Apply diagonalization process rn

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rnGeneral Revisionrn

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