midterm1

midterm1 - Math 107 First Midterm Examination October 3,...

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Math 107 First Midterm Examination October 3, 2008 NAME (Please print) Page Score 2 3 4 5 6 Total Instructions: 1. Do all computations on the examination paper. You may use the backs of the pages if necessary. 2. Put answers inside the boxes (when applicable). 3. Please signify your adherence to the honor code: I, , have neither given nor received aid in completion of this examination. 1
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Gaussian Elimination (26 Points) Score 1. (20 points) Use Gaussian elimination to reduce 2 x 1 + 3 x 2 + x 3 = 4 x 1 + 9 x 2 - 4 x 3 = 2 x 1 - x 2 + 2 x 3 = 3 to reduced row-echelon form. I prefer that we never scale a row; in any case, we always use a single row to create zeros in rows below it: 2 3 1 4 1 9 - 4 2 1 - 1 2 3 2 3 1 4 0 15 / 2 - 9 / 2 0 0 - 5 / 2 3 / 2 1 2 3 1 4 0 15 / 2 - 9 / 2 0 0 0 0 1 If you scale rows (as in the book’s form of Gaussian elimination), then you cannot use the resulting row echelon form to compute a determinant. 2. (6 points) Consider the following row-echelon tableau obtained by Gaussian elim- ination: 2 1 1 0 0 - 5 - 3 0 0 0 0 0 (a) (2 points) Which unknowns in the linear system represented by this tableau are free variables? answer =
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This note was uploaded on 08/03/2009 for the course MATH 107 taught by Professor Trangenstein during the Spring '07 term at Duke.

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midterm1 - Math 107 First Midterm Examination October 3,...

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