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Unformatted text preview: Sample Midterm Exam Math 20F Name: 8/22/08 Section: Read all of the following information before starting the exam: • READ EACH OF THE PROBLEMS OF THE EXAM CAREFULLY! • Show all work, clearly and in order, if you want to get full credit. I reserve the right to take off points if I cannot see how you arrived at your answer (even if your final answer is correct). • A single 8 1/2 × 11 sheet of notes (double sided) is allowed. No calculators are permitted. • Circle or otherwise indicate your final answers. • Please keep your written answers clear, concise and to the poin. • This test has xxx problems and is worth xxx points. It is your responsibility to make sure that you have all of the pages! • Turn off cellphones, etc. • Good luck! 1 2 3 4 5 ∑ 1. ( 0 points ) ( a ) Let A = 1 3 4 2 5 7 1 2 2 , and b = 1 2 3 . Solve A x = b . Answer: By row reduction: x = 3 2 2 . . ( b ) Suppose T 1 1 = 2 3 and T 1 1 = 2 1 . Find the matrix for the linear transformation T . Answer: Note that the hypothesis imply T 1 = 2 2 and T 1 = 1 , so A = 2 2 1 . . ( c ) Define linear independence. Answer: Vectors v 1 ,..., v n are linearly independent if α 1 v 1 + ... + α n v n = implies that α i = 0 for all i . (That is, the only linear combination of v 1 ,..., v n giving the vector is the trivial one taking all coefficients to be zero.) ( d ) Let A = 1 2 2 3 4 2 5 7 . Are the columns of A linearly independent?linearly independent?...
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This note was uploaded on 09/29/2011 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.
 Spring '03
 BUSS
 Math

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