Linear Algebra

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Unformatted text preview: · · + c1 + c0 ). −1 +k Thus n ∈ span({ }). Inductively, if n n+1 ∈ −1 n+k+1 = ±(c +k k+2 span({ }), then + · · · + c1 + n−1 −1 2 c + 0 k+1 ) ∈ span({ }). Thus span({ }) = −1 span({ }) has dimension ≤ . 5.4.18 (a) Note that det( ) = det( − 0I ) = f (0) = a0 . Thus if and only if det( ) = 0 if and only if a0 = 0. is invertible 2 (b) By the Cayley-Hamilton Theorem, we have (−1)n An + an−1 An−1 + a1 A + a0 I = 0. This can be rearranged to give −a0 I = (−1)n An + an−1 An−1 + a1 A. Since A i...
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This note was uploaded on 04/02/2013 for the course MATH 115A 262398211 taught by Professor Fuckhead during the Spring '10 term at UCLA.

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