Course Objectives:

1.         Find solutions of systems of equations using Gaussian elimination, matrix methods, and Cramer's Rule.
2.         Solve systems of linear equations using the inverse matrix method, determine geometrical interpretations in two and three dimensions.
3.         Calculate distances and basic vector arithmetic including sums, scalar multiples, dot products, and cross products in the Euclidean 2-space and 3-Space.
4.         Evaluate orthonormal basis by using Gramm-Schmidt Process.
5.         Compute eigenvalues and eigenvectors.  
 

Topical Outline:

1.         Use Gauss Elimination Method for solutions of systems of equations.
2.         Demonstrate knowledge of Matrices.
3.         Identify matrix method for systems of linear equations.
4.         Solve Systems of equations by using Cramer’s Rule.
5.         Demonstrate the vector algebra in The Euclidean 2-Space and 3-Space.
6.         Construct Linear Transformation from Rm to Rn.
7.         Calculate determinants.
8.         Present vectors in n-dimensional Space.
9.         Conduct vector space.
10.       Identify subspaces of a vector space.
11.       Prove linear independence of vectors.
12.       Find basis of a vector space.
13.       Identify row and column space, and rank.
14.       Find nullify of vector space.
15.       Compute inner product of spaces.
16.       Calculate angle between two inner product spaces.
 17.      Construct orthogonal inner product space.
18.       Perform Gram-Schmidt Process.
19.       Compute eigenvalues and eigenvectors.
20.       Demonstrate characteristic equation for a linear mapping.
21.       Change vector basis.
22.       Diagonalize a square matrix.
23.       Identify orthonormal basis for the vector space.
24.       Construct diagonal Matrices.