Spring 2007 - Mengi's Class - Quiz 1

Spring 2007 - Mengi's Class - Quiz 1 - Quiz 1, Math 20F -...

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Quiz 1, Math 20F - Lecture B (Spring 2007) 1. In this question we want to determine whether there exists a quadratic polynomial in the form p 2 ( x ) = a 1 + a 2 x + a 3 x 2 that passes through the points (1 , 2) and ( - 1 , 4) and, if there are more than one such polynomials, characterize these polynomials. a) (2.5 points) Find a system of 2 linear equations in 3 unknowns whose solution set consists of all triples ( a 1 , a 2 , a 3 ) such that p 2 ( x ) = a 1 + a 2 x + a 3 x 2 passes through (1 , 2) and ( - 1 , 4). Provide also the 2 by 4 augmented matrix associated with this system. Solution Using the constraints that the polynomial has to pass through (1 , 2) and ( - 1 , 4), we have the linear equations p 2 (1) = a 1 + a 2 (1) + a 3 (1) 2 = 2 p 2 ( - 1) = a 1 + a 2 ( - 1) + a 3 ( - 1) 2 = 4 with a 1 , a 2 and a 3 unknowns. The augmented matrix for this system is ± 1 1 1 2 1 - 1 1 4 ² . b) (2.5 points) Row reduce the augmented matrix associated with the system of linear equations in part a) into the reduced echelon form. Using the reduced echelon form decide
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Spring 2007 - Mengi's Class - Quiz 1 - Quiz 1, Math 20F -...

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