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MATH21F09M1sol

MATH21F09M1sol - MATH 21 NOVEMBER 2 2009 EXAM 1.2 Solutions...

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MATH 21 NOVEMBER 2, 2009 EXAM 1.2 — Solutions Instructions Please turn OFF all cell phones, iPods, etc. . There are 5 questions worth a total of 42 points. 100%=40 points. Read all the questions before you begin. Answer the ones you find easiest first . Please write neatly and show all your work. No notes or books. No calculators! Take your time, and check your answers. Good Luck!!! NAME: Zarathustra Problem Score 1 /14 2 /10 3 /6 4 /8 5 /4 Total /40 1
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MATH 21 EXAM 1 FALL 2009 (1) Consider the matrix M = 1 1 - 1 0 1 - 1 0 3 - 2 1 2 2 - 2 1 5 2 1 - 4 3 3 . a. (4 pts) Write down the system of equations whose augmented matrix is M . x 1 + x 2 - x 3 = 1 - x 1 + 3 x 3 - 2 x 4 = 1 2 x 1 + 2 x 2 - 2 x 3 + x 4 = 5 2 x 1 + x 2 - 4 x 3 + 3 x 4 = 3 b. (6 pts) Find the reduced row echelon form of M . M 1 0 - 3 0 - 7 0 1 2 0 8 0 0 0 1 3 0 0 0 0 0 . c. (2 pts) Use your answer to b. to describe the set of solutions to the system in a. x 4 = 3, x 3 = u ( x 3 is free: u is a parameter), x 2 = 8 - 2 u and x 1 = - 7 + 3 u . Or, x 1 x 2 x 3 x 4
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