MA 250 - Linear Algebra

2. Calculate the determinants of matrices and use them in identifying invertible matrices and characteristic polynomials.

3. Use Gauss-Jordan elimination to find inverses of matrices. 

4. Analyze and prove whether sets of vectors in Rn, together with their operations, meet the requirements for vector spaces and subspaces. 

5. Identify important components of vectors spaces such as basis sets, spanning sets, and dimension. 

6. Identify important qualities of matrices such as the rank and row, column, and null spaces.

7. Determine an orthonormal basis of a vector space and using the Gram-Schmidt process. 

8. Find eigenvectors, and eigenvalues, and use them in applications.

9. Perform factorizations of matrices such as LU and QR decomposition and applying the Spectral Theorem.

10. Find the matrix of a linear transformation and compute its range and kernel.

11. Use visual representations such as graphs, charts, or graphics to enhance the meaning of the message that is being communicated. 

12. Complete work accurately, with attention to detail. 

A. Row Reduction and Echelon Forms

II. Matrix Algebra

A. Determinants

B. Inverse Matrix

C. Gauss-Jordan Elimination

III. Vector Spaces

A. Definition of a Vector Space

B. Subspaces and Spanning Sets

C. Basis and Dimension

D. Linear Independence

E. Row, Column, Null Space, and Rank

IV. Orthogonality

A. Projections

B. Subspaces

C. Orthonormal Spaces and the Gram-Schmidt process for Orthonormalization

D. QR Decomposition (Orthogonal/Upper Triangular Factorization)

V. Eigenvalues and Eigenvectors

A. Characteristic Polynomials

B. Diagonalization

C. Eigenspace

D. Symmetric Matrices and the Spectral Theorem

VI. Linear Transformations

A. As Matrices

B. Kernel and Range

C. Applications

Lecture: 10-75%

Technology supplemented instruction: 10-25%

Facilitated discussion: 10-75%