340exam1solfall07

340exam1solfall07 - MATH 340; EXAM # 1, 100 points, October...

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MATH 340; EXAM # 1, 100 points, October 11, 2007 (R.A.Brualdi) TOTAL SCORE : Name: These R. Solutions 1. (12 points; 4 points each) Let A be an m by n matrix with rows α 1 , α 2 , . . ., α m and let B be a matrix with columns β 1 , β 2 , . . ., β n . Then, The entry of AB in position ( i, j ) is: α i · β j The rows of AB are: α 1 · B, . . ., α m · B The columns of AB are: 1 , . . ., Aβ n 2. (8 points) The augmented matrix of a system Ax = b of 4 equations in 5 unknowns x 1 , x 2 , x 3 , x 4 , x 5 has rref (reduced row echelon form) equal to 1 - 1 0 0 1 2 0 0 1 0 3 - 4 0 0 0 1 5 6 0 0 0 0 0 0 Is the system Ax = b consistent ? If so, what is the solution set ? The systems is consistent. The solution set is given by: x 1 = 2 + x 2 - x 5 x 2 = r arbitrary x 3 = - 4 - 3 x 5 x 4 = 6 - 5 x 5 x 5 = s arbitrary 3. (8 points; 4 points each ) Let A be a matrix of size 3 by 4. 1. What
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340exam1solfall07 - MATH 340; EXAM # 1, 100 points, October...

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