MAT 243 - Linear Algebra

Objectives

1. Define a linear equation in n unknowns.
2. Explain an (mxn) systems of Linear Equations.
3. Understand and use Gaussian Elimination to solve systems of Linear Equations.
4. Know the matrices and represent a Linear system in Matrix form.
5. Perform Row or Column operations, Addition, Subtraction, and Multiplication on Matrices.
6. Represent vectors in Rn.
7. Know the properties of Matrix operations.
8. Find the Transpose of a Matrix.
9. Define Linear Independence and non singular matrices.
10. Perform Numerical Integration and Differenciation.
11. Define Identity Matrix.
12. Calculate inverse of a Matrix.
13. Know vector space properties of Rn and perform arithmetic operations on them.
14. Define subspaces of Rn.
15. Verify that subsets are subspaces.
16. Define the Null space of a Matrix.
17. Describe the Range of a Matrix.
18. Obtain Bases for subspaces.
19. Translate the Geometric concept of Dimension into Algebraic terms.
20. Calculate orthogonal and orthonormal Bases.
21. Determine p-dimensional coordinates of a subspace Rn.
22. Perform Linear Transformation from Rn to Rm.
23. Solve the least squares problem in Rn.
24. Find Best Approximation.
25. Find the projection Matrix.
26. Find Eigenvalues and Eigenvectors for Matrices.
27. Define Determinants.
28. Use cofactors to find Minors of an (nxn) Matrix.
29. Use elementary operations to simplify Determinants.
30. Solve problems involving complex Eigenvalues and Eigenvectors.
31. Diagonalize a Matrix.
32. Define and solve Difference Equations.
33. Define and solve systems of Differential Equations.
34. Define and solve problems involving Linear Transformations.
35. Solving systems of Equations using Cramer's Rule.
36. Use Determinants to solve problems involving Wronskians.
37. Find Eigenvalues of Hessenberg Matrices.

Optional

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Syllabus

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Outline

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Text

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Examples of Objectives

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