20f_03w_1be

20f_03w_1be - Math 20F First Midterm January 27, 2003 PRINT...

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Math 20F First Midterm January 27, 2003 PRINT NAME Write version on your blue book and VERSION B 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. (10 pts.) Prove or give a counterexample: (a) If A and B are 2 × 2 matrices, then AB = BA . (b) For every matrix matrix A , the first entry in A T A is non-negative. (In other words, if B = A T A , then b 11 0.) 2. (15 pts.) Let A = 11 - 10 22 3 0 10 0 - 1 00 1 0 . (a) How many solutions does A x =(0100) T have? Justify your answer. (b) How many solutions does A x =(0010) T have? Justify your answer. (c) Either find a b so that A x = b has exactly one solution or explain why this is
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