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Unformatted text preview: =15 x 1 +15 x 230 x 3 +2 x 4 +8 x 5 = 2 2 x 16 x 2 +9 x 32 x 423 x 5 = 1 (c) This ones over the eld C , the complex numbers. x 1 +(2 + 2 i ) x 2 +(7i ) x 3 = 10 + i (3i ) x 1 +(2 + 10 i ) x 2 +(246 i ) x 3 = 3115 i 4 ix 2 +4 x 3 = 88 i (d) This ones over the twoelement eld Z 2 . x 1 + x 3 + x 4 = 0 x 1 + x 2 + x 4 + x 5 = 1 x 1 + x 3 + x 5 = 0 x 1 + x 2 + x 5 = 1 In this case, explicitly list all the solutions. 4. (a) Let A = a b c d be any 2 2 matrix. Show that there is a nonzero vector ~v with A~v = ~ 0 if and only if adbc = 0. (b) Find all complex numbers (if any) such that 1 221 ~v = ~v has a nonzero solution ~v . (c) For each you found in the previous part, nd all vectors ~v such that 1 221 ~v = ~v . 1...
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This note was uploaded on 04/29/2008 for the course MATH 223 taught by Professor Loveys during the Fall '07 term at McGill.
 Fall '07
 Loveys
 Linear Algebra, Algebra, Real Numbers

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