Aug 09, 2020
MT 292 - Introduction to Linear Algebra
Credit Hours: 4
An introduction to linear algebra for students with a strong mathematics background. Topics to be covered include matrices and systems of linear equation, vector spaces, determinants and linear transformations.
Upon completion of this course, the student will be able to:
- solve systems of linear equations. Use matrix methods (Gaussian elimination, inverse matrices, Cramer's Rule);
- carry out matrix computations (add, subtract, multiply) and to solve matrix equations using algebraic techniques;
- define the determinant function for any square matrix and be able to compute the value using a variety of methods (the definition, row reduction, expansion by cofactors);
- use the properties of determinants to simplify determinants;
- do computations with n-dimensional vectors and to generalize these ideas to general vector spaces;
- define, explain, and use the concepts of a spanning set, a linearly independent set, a basis and dimension for any vector space;
- define, explain and use the concepts of row space, column space, null space rank and nullity for any matrix;
- explain the mathematical equivalences between general vector space problems and systems of equations;
- define, explain, and use the concepts of eigenvector and eigenvalue, and use them to decide whether or not a matrix can be diagonalized;
- define, explain, and use the concept of a linear transformation;
- explain the equivalence between linear transformations and matrices; and
- prove and explain elementary results in linear algebra.
Prerequisites: MT 182 or equivalent and/or appropriate mathematics level code.*
S (C, N, S)
*Level code is determined by Mathematics Department placement test and/or successful completion of math courses.