homework_3_solutions

# homework_3_solutions - MA 265 HOMEWORK ASSIGNMENT #3...

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Unformatted text preview: MA 265 HOMEWORK ASSIGNMENT #3 SOLUTIONS #1. Page 94; Exercise 1. Find a row echelon form of each of the given matrices. Record the row operations you perform, using the notation for elementary row operations. (a) A = - 1 2- 5 2- 1 6 2- 2 7 (b) A = 1 1- 1 3 4- 1 5 6- 3- 2- 2 2 Solution: (a) Denote r i as the i th row of A . First we find the leading one in the first row: (- 1) r 1 r 1 : A (- 1) r 1 r 1 = 1- 2 5 2- 1 6 2- 2 7 Now we subtract to eliminate the entries in the first column: (- 2) r 1 + r 2 r 2 : A (- 2) r 1 + r 2 r 2 = 1- 2 5 3- 4 2- 2 7 (- 2) r 1 + r 3 r 3 : A (- 2) r 1 + r 3 r 3 = 1- 2 5 3- 4 2- 3 Next we find the leading one in the second row: (- 1 / 3) r 2 r 2 : A (- 1 / 3) r 2 r 2 = 1- 2 5 1- 4 3 2- 3 We use this to find an echelon form: (- 2) r 2 + r 3 r 3 : A (- 2) r 2 + r 3 r 3 = 1- 2 5 1- 4 3- 1 3 (- 3) r 3 r 3 : A (- 3) r 3 r 3 = 1- 2 5 3- 4 1 1 2 MA 265 HOMEWORK ASSIGNMENT #3 SOLUTIONS (b) Denote...
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## This note was uploaded on 03/11/2010 for the course MA 261A 0026100 taught by Professor ... during the Spring '10 term at Purdue University Calumet.

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homework_3_solutions - MA 265 HOMEWORK ASSIGNMENT #3...

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