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Math254OldQuiz1

# Math254OldQuiz1 - Math 254 Name QUIZ 1 MATH 254 SUMMER 2001...

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Math 254 Name: ________________________ QUIZ 1 MATH 254 - SUMMER 2001 - KUNIYUKI CHAPTERS 1, 2, 3 Show all appropriate work (as we have done in class) for full credit! A scientific calculator is allowed on this quiz. 1) Solve the system below using Gauss-Jordan elimination. Write the solution set in parametric form. (You have room on the back of this sheet.) (20 points) 3 2 6 5 2 3 5 6 4 12 7 16 1 2 3 4 2 3 1 2 3 4 x x x x x x x x x x - + - = - = - - + - = Ï Ì Ô Ô Ó Ô Ô

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1) cont.)
2) Find the matrix X X T ( ) - 1 if X is the matrix 1 1 1 5 3 4 - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ . (15 points) 3) If A is an invertible matrix, find an expression for the solution x to the system A x b = and prove that it is unique (as we have done in class). Assume that all sizes are compatible. (Your proof of uniqueness will not require uniqueness of A - 1 .) (5 points)

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4) Let A be the matrix 1 5 4 0 3 1 4 14 14 - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ . (20 points total) a) Find an LU -factorization of A . (10 points)
b) Use a) to solve the following system. (10 points) x x x x x x x x 1 2 3 2 3 1 2 3 5 4 10

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