midterm_1_solutions

# midterm_1_solutions - MA 35100 MIDTERM EXAM#1 SOLUTIONS...

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MA 35100 MIDTERM EXAM #1 SOLUTIONS Problem 1. Consider the following linear system of equations: ± ± ± ± x + 2 y = 5 3 x + 5 y = 13 ± ± ± ± a. Find the augmented matrix A corresponding to the system. b. Compute its reduced row-echelon form E = rref( A ). c. Find the solution of the linear system. Solution: (a) The augmented matrix of the system is that matrix containing the numerical constants in the system: A = ² 1 2 5 3 5 13 ³ (b) To compute the reduced row-echelon form, we subtract 3 times the ﬁrst row from the second, then divide the second row by - 1: ² 1 2 5 0 1 2 ³ Now subtract 2 times the second row from the ﬁrst: E = ² 1 0 1 0 1 2 ³ (c) This matrix represents the system x = 2 and y = 3, so the solution to the original linear system is ² x y ³ = ² 1 2 ³ Problem 2. Consider the following 2 × 2 matrices: A = ² 0 - 1 1 0 ³ , B = ² 0 1 1 0 ³ , and C = ² 0 1 - 1 0 ³ . a. One of these matrices represents a reﬂection about a line L through the origin. Explain which it is, and give an explicit equation for L in the form y = mx . b. Two of these matrices represent rotations in the coordinate plane. Explain which they are, and give

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## This note was uploaded on 03/31/2012 for the course MA 351 taught by Professor ?? during the Spring '08 term at Purdue.

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midterm_1_solutions - MA 35100 MIDTERM EXAM#1 SOLUTIONS...

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