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solutionsFinalExam - Math 222 - 500 1. Final Exam Dec 13,...

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Final Exam Dec 13, 2006 1 . (25) Define the following: a . L is a linear transformation, L is first of all a function mapping a vector space V into a vector space W with the following additional property: if x u and y u are any two vectors in V and u and U are any two scalars, then L u u x u U U y u U ± u L u x u U U U L u y u U . b . matrix representation of a linear transformation, Let L : V ² W be a linear transformation. Suppose B 1 and B 2 are bases of V and W respectively. Then A is the matrix representation of L with respect to the given bases if ± L u x u B 2 ± A ± x u ² B 1 . c . linearly independent set of vectors, A set of vectors ³ x u i ´ i ± 1 n is linearly independent if whenever c 1 x u 1 U µ c n x u n ± 0 u , then each of the c i ’s must equal 0. d . eigenvector If A is an n ± n matrix and x u u R n , then x u is an eigenvector of A if x u U 0 u and there is a number ² such that Ax u ± ² x u . e
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This note was uploaded on 03/27/2008 for the course MATH 222 taught by Professor Stecher during the Spring '08 term at Texas A&M.

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solutionsFinalExam - Math 222 - 500 1. Final Exam Dec 13,...

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