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Unformatted text preview: 2 . Show that there are scalars α and β such that x n = α ( λ 1 ) n + β ( λ 2 ) n for all n . (c) Give an explicit formula for each of the following recursively deﬁned sequences. x = 2 , x 1 = 3 , x n +2 = x n +1 + 6 x n . x =4 , x 1 = 2 , x n +2 = 8 x n +120 x n . 3. Calculate (by hand, SVP) det 71 38 5 1346 1 3 22 4 4 1 5 . 4. Suppose that A = a b c d e f g h j and B = d * a g e * b h f * c j are matrices with complex entries, and det ( A ) = 4 i , det ( B ) =2 + i . What is det ( C ) if C = g h j 2 idd * 2 iee * 2 iff * (1 + i ) a (1 + i ) b (1 + i ) c ? 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

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