2331_hw4_key - Homework is graded out of 55 5 = 60 points(5...

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1 Math 2331 Homework 4 KEY Problem 1: (2 points each) Which 3 matrices 21 31 32 , , E E E put A into triangular form ? 1 1 2 4 8 0 3 5 0 A = - ; 32 31 21 E E E A U = 21 1 0 0 4 1 0 0 0 1 E = - 31 1 0 0 0 1 0 3 0 1 E = 32 1 0 0 0 1 0 0 2 1 E = - Problem 2: (3 points) If 21 E adds row 1 to row 2 and then 23 P exchanges rows 2 and 3. Which matrix 23 21 M P E = does both operations at once? 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 M     = =       Problem 3: (2 points each) The following matrix needs 3 elimination matrices. What are they? Write both the notation of the matrix (that is, ij E ) and the matrix itself. 2 1 0 0 1 2 1 0 0 1 2 1 0 0 1 2 A = (i) 21 1 0 0 0 1/ 2 1 0 0 0 0 1 0 0 0 0 1 E - = (ii) 32 1 0 0 0 0 1 0 0 0 2 / 3 1 0 0 0 0 1 E = - (iii) 43 1 0 0 0 0 1 0 0 0 0 1 0 0 0 3/ 4 1 E = - Homework is graded out of 55+5 = 60 points.
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