Apr 16, 2024  
2017-2018 Undergraduate Academic Catalog 
    
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2017-2018 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 2830 - Linear Algebra for Math Majors

4 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
  • None
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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