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Dec 26, 2024
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MA 2830 - Linear Algebra for Math Majors4 lecture hours 0 lab hours 4 credits
Course Description
Topics include the use of elementary row operations to solve systems of linear equations, linear independence, matrix operations, inverse of a matrix, linear transformations, vector spaces and subspaces, coordinate systems and change of bases, determinants of matrices and their properties, eigenvalues, eigenvectors, diagonalization, inner product and orthogonality, the Gram-Schmidt Process, and the least-squares problem. Particular emphasis is given to proper mathematical reasoning and presentation of solutions. The students will use MATLAB to explore certain applications. (prereq: MA 1830 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Understand the basic theory of linear algebra
- Apply the basic row operations to solve systems of linear equations
- Solve a matrix equation and a vector equation
- Understand the concept of linear dependence and independence
- Understand matrix transformations and linear transformations and the relationship between them
- Perform all matrix operations, be able to find the inverses of matrices
- Understand concepts of vector space, subspace and basis and be able to change bases
- Describe the column and null spaces of a matrix and find their dimensions
- Find the rank of a matrix
- Be able to find the eigenvalues and corresponding eigenvectors of matrices
- Be able to identify a diagonalizable matrix and diagonalize it
- Understand the relationship between eigenvalues and linear transformations
- Understand the concepts of orthogonality and orthogonal projections
- Apply the Gram-Schmidt Process to produce orthogonal bases
- Find the least-squares solution to a system of linear equations
Coordinator
Dr. Kseniya Fuhrman
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