quiz3-sol

quiz3-sol - From the reduced row echelon form of the...

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Name: MATH227 Quiz 3 (Fall 2006) For full credit, please show all steps in details!! 1. Suppose A is a 4 × 3 matrix and b is a vector in R 3 with the property that A x = b has a unique solution. What can you say about the reduced row echelon form of A ? (4 points) If the equation A x = b has a unique solution, then the associated system of equations does not have any free variables. So every variable is a basic variable, and hence each column of the reduced row echelon form of A has a leading ‘1’. So the reduce echelon form of A must be 1 0 0 0 1 0 0 0 1 0 0 0 . 2. Let A = ± 1 - 2 - 9 5 0 1 2 - 6 ² . Describe all solutions of A x = 0 in parametric vector form. (6 points) Considering the augmented matrix ± 1 - 2 - 9 5 | 0 0 1 2 - 6 | 0 ² R 1 +2 R 2 ± 1 0 - 5 - 7 | 0 0 1 2 - 6 | 0 ²
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Unformatted text preview: From the reduced row echelon form of the augmented matrix, x 1 , x 2 are basic variables and x 3 , x 4 are free variables. The general solution is x 1 = 5 x 3 + 7 x 4 , x 2 =-2 x 3-6 x 4 , x 3 , x 4 are free . Thus, the parametric vector form is x = 5 x 3 + 7 x 4-2 x 3 + 6 x 4 x 3 x 4 = 5 x 3-2 x 3 x 3 + 7 x 4 +6 x 4 x 4 = x 3 5-2 1 + x 4 7 6 1 . 1...
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This note was uploaded on 04/23/2008 for the course MATH 227 taught by Professor Sze during the Fall '06 term at UConn.

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