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2331_hw2_key - Homework is graded out of 50 points Math...

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1 Math 2331- HW 2 Key Problem 1: (2 points each) If ° = ± 1 2 0 1 1 2 0 4 2 ² , ³ = ± 1 3 5 ² , ´ = ± 1 1 1 ² , µ = ± 1 0 0 ² , a) 1 2 0 1 1 1 0 1 0 2 1 0 4 2 0 Ai                 = + + =                         b) 1 2 0 3 1 1 1 1 1 2 4 0 4 2 6 Aw                 = + + =                         c) 1 2 0 7 1 1 3 1 5 2 14 0 4 2 22 Av             = + + =                   Homework is graded out of 50 points.
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2 Problem 2: Consider the following system. ¶ · ¸ = 3 2¶ ¹ 4¸ = 12 a) (3 points) Draw the row picture. Since the lines intersect at (4,1), the solution is (4,1).
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3 b) (3 points) Draw the column picture. Since 1 1 3 4 1 2 4 12 -   + =     , the solution is (4,1). c) (3 points) Write the system in matrix form Ax b = . 1 1 3 2 4 12 x y -  =   d) (3 points) What is the solution of the system? 1 2 2 2 1 1 3 1 1 3 2 4 12 0 6 6 R R R - + - - → 6 6 1 1 3 4 y y x x = = - = = Answer: x=4, y=1.
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4 Problem 3: (Not graded) Solve this system without elimination. Show why your answer works.
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