MAT 264 - Linear Algebra
Linear equations and matrices, vector spaces, inner product spaces, linear independence, linear transformations. Determinants and Cramer's rule, systems of homogeneous equations, Gram-Schmidt process and diagonalization. Eigenvalues and eigenvectors and applications.
Prerequisite: MAT 182 Calculus II w/Analytic Geometry
4 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Solve systems of equations using Gauss-Jordan elimination.
2. Find non-trivial solutions to homogeneous systems of equations.
3. Find the inverse of a matrix by elementary row operations.
4. Compute determinants and solve equations using Cramer's rule.
5. Define a vector space.
6. Determine if a set of vectors form a vector space.
7. Determine if a set of vectors are independent.
8. Determine if a set of vectors span a given vector space.
9. Find the dimension of a vector space and determine if a set of vectors form a basis for the space.
10. Find the dimension of the row space and column space of a matrix.
11. Find the rank of a matrix.
12. Define an inner product space.
13. Use the Gram-Schmidt process to generate an orthogonal and orthonormal basis for a vector space.
14. Diagonalize a matrix using eigenvalues and eigenvectors.
15. Define a linear transformation and show a given transformation is linear.
16. Represent a linear transformation by a matrix.
17. Find the range and kernel of a linear transformation.
18. Use the techniques and concepts of linear algebra in a variety of real-life applications.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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