exam1_sol

# exam1_sol - Exam Midterm Exam 1 Course M340L University of...

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Exam: Midterm Exam 1 Course: M340L Page: 1of 5 University of Texas at Austin Midterm Exam 1 with Solutions. Note: the order of the problems may be diﬀerent than the one in your exam booklet. Detailed solutions are provided on the pages following this one. MC. Solution 1 (4) a b c d e 2 (4) a b c d e 3 (4) a b c d e 4 (4) a b c d e 5 (4) a b c d e 6 (4) a b c d e Pr. Solution 7 (8) [1,1,-2],[1,1,-2],[1,1,-2], e.g. 8 (8) [1 , 0 , 0 , 1] + x 3 [2 , - 2 , 0 , 0] Instructor: Gordan ˇ Zitkovi´ c Semester: Fall 2005

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Exam: Midterm Exam 1 Course: M340L Page: 2of 5 Multiple Choice Questions Question 1. (4pts): Which of the following can not be the number of solutions of a system of linear equations (a) 0 (b) 1 (c) 5 (d) inﬁnitely many (e) none of the above (each can be the number of solutions to a linear system). Solution: The correct answer is (c). If the system is inconsistent, the number of solutions is 0. If it is is consistent, then it either has or doesn’t have free variables. If there are free variables, there are inﬁnitely many solutions, If there are no free variables, the solution is unique. Therefore, 5 can not be the number of solutions of a linear system. / Question 2. (4pts): For what values of h and k is the following system inconsistent? 31 x 1 + 4 x 2 = h - 5 x 1 + x 2 = k (a) h = 1 4 k (b) h = 31 5 k (c) h = - 31 5 k (d) h = - 1 4 k (e) the system is consistent for all values of h and k Solution: The correct answer is (e). The augmented matrix of the system has two pivots in the echelon form
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## This note was uploaded on 08/03/2009 for the course M 91795 taught by Professor Koch during the Spring '09 term at University of Texas.

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exam1_sol - Exam Midterm Exam 1 Course M340L University of...

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