Math254OldFinal

Math254OldFinal - Math 254 Name: _ FINAL MATH 254 - SUMMER...

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Math 254 Name: ________________________ FINAL MATH 254 - SUMMER 2001 - KUNIYUKI Show all appropriate work (as we have done in class) for full credit! A scientific calculator is allowed on this quiz. This final will be scored out of 100 points; the score will then be doubled. You do not have to rationalize denominators or simplify radicals (e.g., 12 2 3 = ). 1) Find the inverse of the matrix A = È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 040 100 002 . (8 points)

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2) Find the determinant of the matrix A = -- 0002 3127 62 31 5004 . (10 points)
3) Let v 1 = (1,2) and v 2 = (3,5). Express (-7,-9) as a linear combination of v 1 and v 2 . There should be no unknowns in your final expression. (10 points) 4) The vectors x , y , and z are three vectors in R n for some fixed n . Prove that if x is orthogonal to both y and z , then x is orthogonal to any linear combination of y and z . (10 points)

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5) The linear transformation TR R : 54 A is defined by T ( x ) = A x , where A = - È Î Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ 10 4 3 01 25 0 000 20 8 6 0 0 3 0 . Find a basis for the Range of T . (10 points)
6) Orthogonally diagonalize the symmetric matrix A = È Î Í ˘ ˚ ˙ 14 41

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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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Math254OldFinal - Math 254 Name: _ FINAL MATH 254 - SUMMER...

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