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Unformatted text preview: Final Review What have we covered since the last midterm? Lots of big, important ideas. Most of them have to do with assigning or changing a basis to a vector space. • Bases (what is a basis, how to check if something is a basis, how to change basis, what “coordinates” of a vector are with respect to some basis, the- orems about bases) • Matrix for a linear transformation (how can we represent linear transfor- mations as matrices with respect to some basis, how matrices of a linear transformation with respect to different bases are related, (i.e., similarity)) • Eigenvalues, eigenvectors, eigenspaces (how to find all of these, what they are good for, diagonalization of linear transformations, theorems) • Symmetric matrices (why they are nicer than most matrices, theorems about them) • Orthonormal bases (why they are nicer than most bases, theorems about them) • Kernel, image, nullity, rank (what they are, theorems about them, how to find them) • Gram-Schmidt (what it is, why we care, how to do it in small cases) Of course, topics like “Basis” are very broad, so it’s hard to write problems representative of all the ideas involved. The best way to study is to try to really understand what a basis is, to know the definitions really well, and why we care about bases (if you understand why we care, you’re a good part of the way to understanding what they are). But in any case, here are some sample non- WebWork type problems – I’ll assume you have a good idea of what WebWork type problems will be on the final. Some of the below problems are easy, some aren’t as easy...there’s a range....
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This note was uploaded on 03/23/2010 for the course MAT 022A taught by Professor Pon during the Spring '10 term at UC Davis.
- Spring '10
- Vector Space