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Apr 19, 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, linear transformations, and the relationship between them
- Perform 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
- Find the eigenvalues and corresponding eigenvectors of matrices
- 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
Prerequisites by Topic Course Topics
- Systems of linear equation, solutions using matrices, row operations
- Vector and matrix equations
- Solution sets of linear systems
- Linear independence
- Linear transformations
- Matrix algebra
- Subspaces, dimension, and rank
- Determinants and their properties
- Real eigenvalues and eigenvectors
- Diagonalization
- Complex eigenvalues
- Inner products and orthogonality
- Orthogonal projections
- The Gram-Schmidt Process
- Least-squares solutions
Coordinator Kseniya Fuhrman
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