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HW1 - AMS210.01 Homework 1 Andrei Antonenko Due at the...

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AMS210.01. Homework 1 Andrei Antonenko Due at the beginning of the class, February 17, 2003 1. Solve each of the the following equations: (a) 5 x = log 3 2 (b) 0 x = 3 (c) 0 x = 0 2. Solve each of the following equations. Consider a as a parameter and don’t forget different cases for different values of it: (a) 6 x = a (b) ax = 2 (c) ax = 2 a 3. Write the solution set of each of the following equations and find 2 particular solutions: (a) x 1 + x 2 = 6 (b) 2 x 1 - x 2 + 4 x 3 = - 1 4. Solve the following systems in echelon form. Also, for each system which has infinitely many solutions, specify 1 numerical solution. (a) x 1 + 3 x 2 - x 3 = 13 x 2 + 3 x 3 = 10 - 2 x 3 = - 4 (b) x 1 - 4 x 2 + 10 x 3 = 3 15 x 2 + 3 x 3 = 10 0 = 2 (c) x 1 + 4 x 2 + x 3 = 15 - 3 x 3 = - 3 0 = 0 1
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(d) 2 x 1 - x 2 + x 3 = 15 x 2 + 2 x 3 + 2 x 4 = 10 2 x 4 = 6 (e) 2 x 1 + 2 x 2 + x 3 - x 4 = 4 x 3 + 3 x 4 = 8 5. Find the elementary operation needed to get from the first system to the second one: (a) x 1 + 2 x 2 + x 3 = 9 2 x 1 - x 2 + 3 x 3 = 5 3 x 1 + x 2 - x 3 = 4 x 1 + 2 x 2 + x 3 = 9 3 x 1 + x 2 - x 3 = 4 2 x 1
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