B the given vector is not in the span of the other

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Unformatted text preview: are linearly dependent. b) The given vector is not in the span of the other two vectors. 2) 2 −20 8 −39 22 −5 −3 4 −6 , BA = AB = 4 19 −19 32 −17 10 −15 7 13 −1 −3 8 19 −14 −5 −4 54 −12 8 −12 35 −1 15 T −1 6 11 and AT A = −12 26 −16 2 , AA = 8 −16 11 −3 15 11 55 −12 2 −3 5 3) 0 0 A2 = 0 0 0 0 0 0 2 10 00 0 0 0 4 , A3 = 0 0 0 0 00 00 0 0 0 0 8 00 0 0 0 , A4 = 0 0 0 0 00 4) a) not invertible b) 5) a) 1/3 1/2 − 1/6 −4/9 −1/6 7/18 2/9 −1/6 1/18 −2 3 −6 −3 1 −1 2 2 1 −1 2 1 5 −7 15 8 1 0 0 0 0 0 0 , 0 0 b) −26 13 9 68 6) a) b) c) 1 0 0 0 0 0 1 0 0 −1/5 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 −7 10 01 00 0 0 0 1 0 1 0 0 0 0 0 1 7) NOTE: the answer provided is not unique. To check if the problem is solved correcly, multiply the matrices you obtained and compare it with the given matrix. ￿ ￿￿ ￿￿ ￿￿ ￿ 1 −5 10 10 1 −5 = · · 20 21 0 10 01 2...
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This note was uploaded on 03/07/2013 for the course MATH 0280 taught by Professor Wang during the Spring '08 term at Pittsburgh.

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