Linear Algebra September 2015 practice var1.pdf

Linear Algebra September 2015 practice var1.pdf - Linear...

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PRACTICE EXAM Linear Algebra, Midterm NAME: Q.# 1 2 3 4 5 6 7 8 9 10 ANSWER S E C T I O N I: M U L T I P L E C H O I C E Directions: Each of the following problems is followed by five choices. Select the best choice and put the corresponding mark into the answer sheet above. Don’t forget to put in your name. Remember that incor- rect answers are penalized by - 0 . 25 points, while correct answers are rewarded with +1 . 00 points. There is no penalty for answers left blank. You may write in any part of this booklet. There are additional pages you may use as a scrap paper. If you wish, you may detach them gently, without unstapling the booklet. This booklet is to be turned in at the end of the exam. Calculators may NOT be used at any part of the exam. Time reserved for this section is: 30 min. 1. Let a , b , and c be three linearly independent vectors. Which of the following MUST be true? I. a + b , b + c , a + c are linearly independent II. a - b , b - c , a - c are linearly dependent III. λa , b , and c are linearly independent for all λ R . (A) I only (B) I and II (C) II and III (D) I, II, and III (E) None of the above
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