Dec 10, 2023
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
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.
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