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Unformatted text preview: MATH 54, mock final test. All the necessary work to justify an answer and all the necessary steps of a proof must be shown clearly to obtain full credit. Partial credit may be given but only for significant progress towards a solution. Show all relevant work in logical sequence and indicate all answers clearly. Cross out all work you do not wish considered. 2 pages of notes are allowed. Books and electronic devices are not allowed during the test. 1. Determine for which values of b 1 , b 2 , b 3 the system 2 x 1- 4 x 2- 2 x 3 = b 1- 5 x 1 + x 2 + x 3 = b 2 7 x 1- 5 x 2- 3 x 3 = b 3 has a solution. 2. Let T : IP 2 → IR 3 be the linear map taking a polynomial of degree at most 2 to its values at the points- 1, 0 and 1: T ( p ) := p (- 1) p (0) p (1) . (a) Write the matrix of T in the standard bases. (b) Using the result of (a), find a polynomial f ∈ IP 2 such that f (- 1) = 1, f (0) = 0, f (1) = 2....
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This document was uploaded on 01/07/2012.
- Winter '08