Linear Algebra October 2017 practice var1.pdf

Linear Algebra October 2017 practice var1.pdf - Linear...

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PRACTICE EXAM Linear Algebra, Final Exam 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. Incorrect 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: 45 min. 1. Which of the following numbers is NOT an eigenvalue of the matrix 1 4 1 - 1 1 3 7 6 - 5 - 4 - 5 1 - 5 4 1 5 ? (A) -1 (B) -4 (C) 3 (D) 5 (E) 6 2. Let A be a diagonalizable matrix such that A k = E for some k , where E is the identity matrix. Which of the following MUST be true? I. All eigenvalues of A are equal to 1 by absolute value II. A = E III. A 2 = E 3. Let A be an invertible 3 × 3 matrix. If the 1 st row of A is added to the 3 rd row, then in A - 1 (A) the 3 rd row will be subtracted from the 1 st row (B) the 1 st row will be subtracted from the 3 rd row (C) the 1 st column will be subtracted from the 3 rd column (D) the 3 rd column will be subtracted from the 1 st
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