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Unformatted text preview: M341 Homework Solution 4 Section 2.1  1(b) 3 3 2 6 4 3 2 1 1 23 38 11 (I): 1 1 3 1 1 1 2 3 6 4 3 2 1 1 23 3 38 11 (II): 2 6 1 + 2 (II): 3 2 1 + 3 1 1 2 3 2 1 1 1 3 23 3 8 13 3 (I): 2 1 2 2 1 1 2 3 1 1 2 1 1 3 23 3 4 13 3 (II): 3 2 + 3 1 1 2 3 1 1 2 1 6 23 3 4 1 3 (I): 3 6 3 1 1 2 3 1 1 2 1 23 3 4 2 Therefore, x 3 = 2 , x 2 = 4 1 2 x 3 = 5 , and x 1 = 23 3 + 2 3 x 3 + x 2 = 4 . The system is consistent and it has a unique solution (4,5,2). Section 2.1  1(d) 2 3 4 1 8 5 2 4 5 9 13 3 4 3 2 2 17 47 44 25 (I): 1 1 2 1 1 3 2 2 1 2 8 5 2 4 5 9 13 3 4 3 2 2 17 2 47 44 25 (II): 2 8 1 + 2 (II): 3 5 1 + 3 (II): 4 4 1 + 4 1 3 2 2 1 2 7 14 3 2 3 1 2 3 6 17 2 21 3 2 9 (I): 2 1 7 2 1 3 2 2 1 2 1 2 3 2 3 1 2 3 6 17 2 3 3 2 9 (II): 3 3 2 2 + 3 (II): 4 3 2 + 4 1 3 2 2 1 2 1 2 1 2 17 2 3 3 (I): 3 2 3 1 3 2 2 1 2 1 2 1 17 2 3 6 Therefore, x 4 = 6 , x 3 = c , x 2 = 3 + 2 x 3 = 3 + 2 c , and x 1 = 17 2 + 1 2 x 4 2 x 3 + 3 2 x 2 = 7 + c . The system is consistent and the complete solution set is { (7 + c, 3 + 2 c, c, 6)  c R } Three particular solutions are (7 , 3 , , 6) , (6 , 5 , 1 , 6) and (8 , 1 , 1 , 6) obtained by substituting c = 0 , 1 and 1 . Section 2.1  1(f) [ 5 5 15 3 2 2 6 1 34 12 ] (I): 1 1 5 1 [ 1 1 3 3 5 2 2 6 1 34 5 12 ] (II): 2 2 1 + 2 [ 1 1 3 3 5 1 5 34 5 8 5 ] (I): 2 5 2 [ 1 1 3 3 5 1 34 5 8 ] Therefore, x 4 = 8 , x 3 = c , x 2 = b , and x 1 = 34 5 + 3 5 x 4 + 3 x 3 + x 2 = 2 + 3 c + b . The system is consistent and the complete solution set is { ( 2 + b + 3 c, b, c, 8)  b, c R } 1 Three particular solutions are ( 2 , , , 8) , ( 1 , 1 , , 8) and (1 , , 1 , 8) obtained by substituting b = , c = 0 , b = 1 , c = 0 and b = 0 , c = 1 ....
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This note was uploaded on 12/05/2011 for the course M 341 taught by Professor Hietmann during the Spring '08 term at University of Texas at Austin.
 Spring '08
 HIETMANN

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