Math254Final

# Math254Final - Math 254 Name: _ FINAL MATH 254 - SUMMER...

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Math 254 Name: ________________________ FINAL MATH 254 - SUMMER 2002 - KUNIYUKI GRADED OUT OF 100 POINTS ¥ 2 = 200 POINTS TOTAL Circle your final answers! Show all work and simplify wherever appropriate, as we have done in class! A scientific calculator and an appropriate sheet of notes are allowed on this exam. Assume that n represents a positive integer. 1) Find A 10 if A = - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 10 0 020 00 2 . (3 points) 2) Find the determinant below. (10 points) 23 30 112 0 05 00 34 13 1 4 0 2 10 20 1 -- -

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3) If A is a 44 ¥ matrix, and A = 10 , then find 3 A . (3 points) 4) Let v 1 = 0360 ,,, () , v 2 = 0246 , and v 3 = 112 1 ,, , -- . Express 4 121 1 , -- - as a linear combination of v 1 , v 2 , and v 3 . The weights in this linear combination must be given as specific real numbers; don’t just leave them as "" c i s . (12 points)
5) Find the angle between the vectors 133 ,, () and 21 4 - . Round off your answer to the nearest tenth of a degree. (For maximum accuracy, don’t round off until the end.) (8 points) 6) TR R : 43 Æ is a linear transformation such that TA vv = , where A is the matrix below. (6 points total; 2 points each) A = - - È Î Í Í Í ˘

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## This note was uploaded on 09/08/2011 for the course MATH 254 taught by Professor Howard during the Spring '09 term at Mesa CC.

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Math254Final - Math 254 Name: _ FINAL MATH 254 - SUMMER...

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