homework set 7-Solutions - B ˙ ILKENT UNIVERSITY...

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Unformatted text preview: B ˙ ILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set 1 # 7 U. Mu˘gan June 20, 2008 Homework problems from the 2 nd Edition, SECTION 3.3 3 (3) ) 2 Let A = • 3 7 15 2 5 11 ‚ Do the following row operations: • 3 7 15 2 5 11 ‚ , (- R 2 + R 1 ) → • 1 2 4 2 5 11 ‚ , (- 2 R 1 + R 2 ) → • 1 2 4 0 1 3 ‚ , (- 2 R 2 + R 1 ) → E = • 1 0- 2 0 1 3 ‚ . NOTE THAT: The reduced row-echelon form of a matrix is UNIQUE , so different sequence of elementary row operations should produce the same reduced row-echelon form of the given matrix. 9 (9) ) Let A = 5 2 18 0 1 4 4 1 12 Do the following row operations: R 1- R 3 , R 3- 4 R 1 , R 3 + 3 R 2 , and R 1- R 2 and get E = 1 0 2 0 1 4 0 0 0 . NOTE THAT: The reduced row-echelon form of a matrix is UNIQUE , so different sequence of elementary row operations should produce the same reduced row-echelon form of the given matrix. 13 (13) ) Let A = 2 7 4 0 1 3 2 1 2 6 5 4 Do the following row operations: Swap( R 1 , R 2 ), R 2- 2 R 1...
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homework set 7-Solutions - B ˙ ILKENT UNIVERSITY...

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