Topics Covered:WRITING UP HOMEWORK SOLUTIONS: You are expected to show all essential steps in solving a problem. Draw appropriate figures. If in doubt, PUT IT IN! Make your solution flow. Ask yourself the question: "If I were the reader, how would I score this problem?'' Numerical answers alone, single words "yes" or "no", etc., are NEVER, EVER acceptable as complete answers. One of the skills you are expected to learn in this class is that of communicating mathematics clearly and completely in writing. Writing up homework exercises is your opportunity to hone these skills. Your grade depends on it!
Linear equations and matrices:
Systems of linear equations, row reduction and echelon forms, vector
equations, matrix equations, solution sets, linear independence,
linear transformations and matrix representations (7 lectures).
Matrix algebra:
Basic operations, inverses, characterizations of invertible matrices
(3 lectures).
Introduction to determinants:
Definitions, properties, applications (3 lectures).
Vector spaces:
Definitions, subspaces, null spaces, column spaces, linear
transformations, linear independence, bases, dimension, rank
change of basis, a finite example (8 lectures).
Eigenvalues and eigenvectors:
Definitions, computations, the characteristic equation, diagonalization
(3 lectures).
Orthogonality:
Inner product, length, orthogonal sets, Gram-Schmidt (3 lectures).
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