MT 292 - Introduction to Linear Algebra

• 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.