Math254OldQuiz1Sols

# Math254OldQuiz1Sols - QUIZ 1 SOLUTIONS MATH 254 SUMMER 2001...

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QUIZ 1 - SOLUTIONS MATH 254 - SUMMER 2001 - KUNIYUKI CHAPTERS 1, 2, 3 1) The given equations are already in standard form, and the like terms are lined up. Now, write the corresponding augmented matrix and use row operations to obtain the reduced row-echelon (RRE) form. 3 6 - - - - - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 26 01 3 41 2 5 0 7 2 5 16 We can use the " 3 " to turn the " 6 " into a "0". Let's add (-2) times the first row to the third row. RR R 31 3 2 +- () A Old R 3 6- 4 1 2 - 7 1 6 (-2) R 1 -6 4 -12 10 -4 New R 3 0003 1 2 32 6 5 0 2 5 - - - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 00 03 1 2 Now, divide Row 3 through by 3 to change the " 3 " into a "1". R 3 33 3 or 1 3 A 6 01 30 2 5 - - - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 00 0 5 14 This matrix is almost in row-echelon form (except for the fact that the "3" in the upper left corner should be a "1"). Still, we can "eliminate up" at this point. Let's turn the " -5 " into a "0" by adding 5 times Row 3 to Row 1. RRR 131 5 +A Old R 1 3- -5 2 5 R 3 0005 2 0 New R 1 0 2 2

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32 6 0 2 2 - -- È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 01 3 00 0 0 1 5 4 Now, turn the " -2 " into a "0" by adding 2 times Row 2 to Row 1. RRR 121 2 +A Old R 1 3- 26 0 2 2 2 R 2 02 - 60 -10 New R 1 3000 1 2 30 00 1 2 0 1 5 4 È Î Í Í Í ˘ ˚ ˙ ˙ ˙ Now, divide Row 1 through by 3 to change the " 3 " into a "1". R RR 1 11 3 or 1 3 A 10 00 4 0 1 5 4 È Î Í Í Í ˘ ˚ ˙ ˙ ˙ We now have the reduced row-echelon (RRE) form of the original augmented matrix.
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## This note was uploaded on 09/08/2011 for the course MATH 254 taught by Professor Howard during the Spring '09 term at Mesa CC.

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Math254OldQuiz1Sols - QUIZ 1 SOLUTIONS MATH 254 SUMMER 2001...

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