quiz1_S2005_solns

quiz1_S2005_solns - MATH 202 - QUIZ # 1 Covers Chapter 1...

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Unformatted text preview: MATH 202 - QUIZ # 1 Covers Chapter 1 and Chapter 2 of the text Time: 60 minutes 1. (10 points) Find the intersection of the three planes x + y + z = 3 2 x − y + 2 z = − 2 4 x + y + 4 z = 4 Interpret your answer geometrically. Form the augmented matrix and reduce it completely: 1 1 1 3 2 − 1 2 − 2 4 1 4 4 −→ . . . −→ 1 0 1 1 / 3 0 1 0 8 / 3 0 0 0 So the three planes intersect in a line, given parametrically by x y z = 1 / 3 8 / 3 + t − 1 1 2. (10 points) For what values of b does the matrix equation 1 1 1 2 7 7 4 9 b 2 x y z = 1 2 b + 1 have (a) infinitely many solutions? (b) no solutions? (c) exactly one solution? (Justify your answers.) Row reduce the augmented as much as possible: 1 1 1 1 2 7 7 2 4 9 b 2 b + 1 −→ . . . −→ 1 0 1 0 1 1 0 0 b 2 − 9 b − 3 We can divide by b 2 − 9 provided that this quantity is not zero. So for all b except ± 3 we get 1 0 0 1 0 1 0 − 1 / ( b + 3) 0 0 1 1 / ( b + 3) Thus for b negationslash = ± 3 we get a unique solution.3 we get a unique solution....
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This note was uploaded on 04/28/2008 for the course MAT 202 taught by Professor Staff during the Spring '08 term at Princeton.

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quiz1_S2005_solns - MATH 202 - QUIZ # 1 Covers Chapter 1...

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