t2 previous math 1025

t2 previous math 1025 - York University Faculty of Arts,...

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Unformatted text preview: York University Faculty of Arts, Faculty of Science Math 1025 Class Test 2 NAME (print): SIGNATURE: (Family) (Given) STUDENT NUMBER: Instructions: 1. Time allowed: 50 minutes 2. There are 5 questions on 6 pages. 3. Answer all questions. 4. Your work must justify the answer you give. 5. No calculators or other aids permitted. Question 1 2 3 4 5 Total Points 5 18 6 5 6 40 Marks MATH 1025 Test 2 Page 1 February 25, 2005 1. (5 points) Write the determinant of the matrix 0 0 0 −3 2 0 5 0 0 0 0 0 3 1 0 0 0 0 0 −2 2 0 0 0 0 as a product of its nonzero signed elementary products and compute its value. MATH 1025 2. Let Test 2 0 1 A= 1 1 2 1 1 1 4 2 2 1 6 1 . −1 2 Page 2 February 25, 2005 (a) (6 points) Compute the determinant of A. MATH 1025 (b) (6 points) Find the 2-3 entry of A−1 . Test 2 Page 3 February 25, 2005 MATH 1025 Test 2 Page 4 February 25, 2005 (c) (6 points) Use Cramer’s rule to find the value of d where 2b + 4c + 6d = a + b + 2c + d = a + b + 2c − d = a + b + c + 2d = 0 0 1 0 (Only find d. You must use Cramer’s rule. No marks will be given if you use any other method.) MATH 1025 ￿ ￿ ￿ ￿ 3. (6 points) Given that ￿ ￿ ￿ ￿ a e i m b f j n c g k o d h l p Test 2 ￿ ￿ ￿ ￿ ￿ = −3, find ￿ ￿ ￿ 3b −n + b j − 2f f Page 5 February 25, 2005 ￿ ￿ 3a ￿ ￿ −m + a ￿ ￿ i − 2e ￿ ￿ e 3c −o + c k − 2g g 3d −p + d l − 2h h ￿ ￿ ￿ ￿ ￿. ￿ ￿ ￿ MATH 1025 Test 2 Page 6 February 25, 2005 4. (5 points) Let A and B be 3 × 3 matrices with determinants |A| = −3 and |B | = 2. Compute the determinant | − 2AT B 2 A−1 | 5. (a) (2 points) Find a unit vector parallel to the vector (−4, 0, 3). −→ (b) (4 points) Let ￿ and ￿ be vectors in R3 with ￿￿ ￿ = 2 and ￿ · ￿ = −1. Find all numbers a such u v v uv that the vector ￿ + a￿ is orthogonal to ￿ . (Hint: consider (￿ + a￿ ) · ￿ .) u v v u vv The end ...
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This note was uploaded on 09/28/2010 for the course MATH 1025 taught by Professor Tammie during the Fall '10 term at York University.

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