A2 - Math 235 Assignment 2 Due: Wednesday, May 19th I 1....

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Unformatted text preview: Math 235 Assignment 2 Due: Wednesday, May 19th I 1. For each of the following linear transformations, determine a geometrically natural basis B and determine the matrix of the transformation with respect to B. 3) Perp(2,1,—2) b) reflagyg) 2. Let V be an n dimensional vector space and define the linear operator L : V ——> V by L07) : 27. Prove that [L]B : I for any basis B of V. 3. Let V be an n dimensional vector space with basis B and let S be the vector space of all linear operators L : V ——> V. Define T : S ——> M(n, n) by T(L) : [L]B. Prove that T is a linear mapping. Use MATLAB to complete the following questions. You do not need to submit a printout of your work. Simply use MATLAB to solve the problems, and submit written answers to the questions along with the rest of your assignment. ' For questions that involve a set of vectors, enter each vector separately, giving it a name (e.g., 51, S2, s3) and then construct any required matrices from these vectors (e. g., A : [51 S2 53]). This will make it easier for you to work with the various elements. Matrix Representation of a Linear Mapping Let L : R6 -—> R6 be the linear mapping L[(a1, (12, 0,3, (14, a5, (16)] = (3a1 — 2% + 5613 + 3a4 + 2% + 2%, 4611 + 5G4 + 3615 — 5616, 5612 + 3% + 2a4 + 3% — 2a6, 5a1 + 5a2 — 4a3 — 504 — a5, 5611 —' 303 + 3615, a1 + 2G2 + a3 + 2614 + a5 ‘l" 2615) (a) Find A, the matrix representation of the linear mapping L, with respect to the basis, 8, where B :{ (17070307071))(1>0a170a170)7(—17~170707—17~1)> (07 07 _1) _17 03 0)) (07 27 —2) 2) —2> 0)) (1) 2707 1) 27 } (b) Use A to find [L(v)]3 where [vlg = (4, 1, —3, —3, —1,2). ...
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This note was uploaded on 11/30/2010 for the course MATH 235/237 taught by Professor Wilkie during the Spring '10 term at Waterloo.

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A2 - Math 235 Assignment 2 Due: Wednesday, May 19th I 1....

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