winter 2007assign2-sol

# winter 2007assign2-sol - MATH235 SOLUTIONS TO ASSIGNMENT 2....

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Unformatted text preview: MATH235 SOLUTIONS TO ASSIGNMENT 2. 1. Section 3.1 14) Compute the determinant of the following matrix by cofactor expansions. At each step choose a row or a column that involves the least amount of computation. 6 3 2 4 9- 4 1 8- 5 6 7 1 3 4 2 3 2 Solution. 6 3 2 4 9- 4 1 8- 5 6 7 1 3 4 2 3 2 = 1 * 6 3 2 4 9- 4 1 3 4 2 3 2 = 3 * 3 2 4- 4 1 2 3 2 = 3 * 3 *- 4 1 3 2 + 2 * 2 4- 4 1 = 3 * (3 * (- 4 * 2- 3 * 1) + 2 * (2 * 1- (- 4) * 4)) = 9 . Section 3.2 10) Find the determinant of the following matrix by row reduction to echelon form. 1 3- 1- 2 2- 4- 1- 6- 2- 6 2 3 9 3 7- 3 8- 7 3 5 5 2 7 Solution. 1 1 3- 1- 2 2- 4- 1- 6- 2- 6 2 3 9 3 7- 3 8- 7 3 5 5 2 7 = 1 3- 1- 2 2- 4- 1- 6 3 5- 2 8- 1- 4 8 2 13 R 3 + 2 * R 1 → R 3 R 4- 3 * R 1 → R 4 R 5- 3 * R 1 → R 5 = 1 3- 1- 2 2- 4- 1- 6 3 5- 4 7- 7 1 R 4 + R 2 → R 4 R 5 + 2 * R 2 → R 5 =- 1 * 1 3- 1- 2 2- 4- 1- 6- 4 7- 7 3 5 1 ( R 4 <- > R 3 ) =- 1 * 1 * 2 * (- 4) * 3 * 1 = 24 . 22) Use the determinant to find out if the following matrix is invertible. 5- 1 1- 3- 2 5 3 Solution. 5- 1 1- 3- 2 5 3 = 5 * (- 3 * 3- (- 2) * 5)- 1 * (0 * 3- (- 1) * 5) = 0 The matrix is not invertible since the determinant is zero....
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## This note was uploaded on 05/23/2010 for the course MATH 235 taught by Professor Celmin during the Winter '08 term at Waterloo.

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winter 2007assign2-sol - MATH235 SOLUTIONS TO ASSIGNMENT 2....

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