Unformatted text preview: G )? Explain. 4. Consider the permutation representation of U (15) for which 2 7→ (1 2 3 4) and 14 7→ (5 6). (a) Find the image of each element of U (15) under this representation. (b) Find a matrix representation of U (15) using 6 × 6 permutation matrices. (c) Consider the following six vectors in R 3 : v 1 = (1 , , 0) v 2 = (0 , 1 , 0) v 3 = (1 , , 0) v 4 = (0 ,1 , 0) v 5 = (0 , , 1) v 6 = (0 , ,1) . Use these vectors to ﬁnd a 3 × 3 matrix representation of U (15)....
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 Spring '09
 Math, Algebra, nonzero complex numbers

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