Montgomery College 2019-2020 Catalog 
    Oct 22, 2019  
Montgomery College 2019-2020 Catalog
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MATH 284 - Linear Algebra

Basic concepts of linear algebra including vector spaces, linear equations and matrices, determinants, linear transformations, similar matrices, eigenvalues, and quadratic forms. PREREQUISITE(S): A grade of C or better in MATH 182  or consent of department. For computation of tuition, this course is equivalent to five semester hours. Five hours each week. Formerly MA 284.

4 semester hours

Course Outcomes:
Upon course completion, a student will be able to:

  • Determine whether solutions of a linear system Ax = b exist. If so, determine whether the solution is unique and find a basis for the solution space.
  • Explain what it means for a set of vectors to be a subspace of Rn. Verify that a given set does or does not satisfy the defining properties of a subspace.
  • Demonstrate an understanding of the concepts of linear independence, spanning, and basis. Determine whether a given set of vectors is linearly independent and/or spans a given subspace. Produce a basis for a given subspace of Rn.
  • Perform matrix calculations, applying the rules of matrix algebra.
  • Find the column space, row space, and null space of a matrix. Show an understanding of the relationship between the dimension of the null space, the rank, and the number of columns of the matrix.
  • Define what it means for a function to be a linear transformation from Rn to Rm. Describe the kernel and range of a given linear transformation.
  • Produce the eigenvalues and associated eigenspaces for a given matrix. Explain geometrically the result of multiplying an eigenvector by the matrix.
  • Apply the dot product and its properties to problems of orthogonality, the magnitude of vectors, and the distance between vectors. Produce orthogonal bases of subspaces of Rn.
  • Use the techniques and theory of linear algebra to model various real-world problems. (Possible applications include: curve fitting, computer graphics, networks, discrete dynamical systems, systems of differential equations, and least squares solutions.)
  • Effectively communicate the concepts and applications of linear algebra using the language of linear algebra in a mathematically correct way.
  • Use advanced software tools (e.g., Maple, MATLAB, Mathematica) to solve problems in linear algebra.

Click here for the Fall 2019 Class Schedule

Click here for the Extended Winter 2020 Class Schedule

Click here for the Winter 2020 Class Schedule

Click here for the Spring 2020 Class Schedule

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