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Practice Midterm 1-1

Practice Midterm 1-1 - Math 20F First Midterm PRINT NAME...

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Math 20F First Midterm January 27, 2003 PRINT NAME Write version on your blue book and VERSION A hand in this exam inside your blue book. There are a total of 40 points possible. No BOOKS, NOTES or CALCULATORS are allowed. You must show your work to receive credit. 1. (4 pts.) Fill in the following blanks. (a) If A is an n × n matrix and there is a matrix B such that , we call B the inverse of A . (b) If A and B are matrices such that a ij = b ji for all i and j , we call B . 2. (15 pts.) Let A = 1 0 - 1 0 0 0 0 1 1 1 0 - 1 2 2 0 3 . (a) How many solutions does A x = (1 0 0 0) T have? Justify your answer. (b) How many solutions does A x = (0 0 0 1) T have? Justify your answer. (c) Either find a b so that A x = b has exactly one solution or explain why this is impossible. 3. (10 pts.) Prove or give a counterexample:
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