MATH 205 Linear Algebra (5 credits)

1. Solve a system of linear equations via elimination or a matrix inverse and interpret the solution set geometrically and algebraically. 
2. Compute matrix operations (addition, subtraction, and multiplication), matrix inverses, and matrix determinants without technology. 
3. Analyze vector spaces and their properties, including finding bases and determining whether a subset is a subspace. 
4. Analyze linear transformations, including whether they are injective, surjective, or isomorphisms, by identifying the kernel and image, making connections to the nullspace and column space of a matrix, and interpreting them geometrically when in R^2 and R^3. 
5. Determine eigenvalues, eigenvectors, and diagonalization of matrices when possible. 
6. Identify and explain equivalent conclusions about singular and nonsingular matrices, existence and uniqueness of solutions, bases for R^n, linear transformations, and diagonalization. 
7. Write proof sketches and provide counterexamples when appropriate. 

Critical, Creative and Reflective Thinking: Graduates will evaluate, analyze, synthesize, and generate ideas; construct informed, meaningful, and justifiable conclusions; and process feelings, beliefs, biases, strengths, and weaknesses as they relate to their thinking, decisions, and creations.

Effective Communication: Graduates will be able to craft and exchange ideas and information in a variety of situations, in response to audience, context, purpose, and motivation.

Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50

Potential Methods
Written or Online Homework
Group Activities or Discussions
Presentations
Peer review
Projects
Quizzes or Exams