Introductory treatment of vector, matrices, matrix operations, linear systems, determinants, eigenvalues, eigenvectors, and complex numbers, with emphasis on applications for all topics.
Hours: 60 (Lecture Hours: 3; Laboratory Hours: 1)
Total Weeks: 15
One of Principles of Mathematics 12, Pre-Calculus 12, OR MATH 050.
- Matrix Algebra
- Vector Spaces
- Eigenvalues and Eigenvectors
- Orthogonality and Least Squares
Upon successful completion of this course, a student should be able to:
- Perform operations on vectors in n-space, in particular, for n equals 2 and 3, including addition, scalar multiplication, dot and cross products, and use it to solve a variety of geometrical problems including length, angles, lines and planes.
- Solve systems of linear equations using the method of Gauss-Jordan elimination.
- Perform matrix operations including addition, subtraction, scalar multiplication and inversion.
- Evaluate determinants using row/column reduction and cofactor expansion. Understand the Cramer’s rule and its theoretical importance.
- Reproduce the theory of abstract vector spaces using the axiomatic approach. Solve various problems regarding subspaces, linear independence, bases and dimensions, and rank.
- Solve problems designed to promote understanding of linear maps, linear transformations, nullspaces and ranges, eigenvalues and eigenvectors, similarity and diagonalization.
- Restate the axiomatic approach to Euclidean Spaces (Inner Product Spaces) including orthogonal bases, orthogonal projections and orthogonal subspaces and solve related problems.
- Perform basic arithmetic operations on complex numbers and complex matrices.
Grading System: Letters
Passing Grade: D (50%)
Percentage of Individual Work: 100
Textbooks are subject to change. Please contact the bookstore at your local campus for current book lists.