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More Sample problems - 2 Math1502Q2Ans.nb Math 1502 Problem...

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Unformatted text preview: 2 Math1502Q2Ans.nb Math 1502 Problem 2 (10 points) Find a parametrization of the line that is the intersection of the planes P: x - 2 y - z = 4 and Ans Q: 2x + y + z = 2. There are many different ways to do this. Solve 8 x 5 Let z 8 x 5 t and go : t ,y 5 3 2 t,z t x z ,y 5 2y z 3 2 z 4, 2 x y z 2, x, y Or how about this? eqns x 2y x z 2y z y 4, 2 x z 2 y z 2 4, 2 x 0 y eqns x .z 2y 4, 2 x .z 6 ,y 5 2 0, x, y Solve eqns 8 x 5 So one point in the intersection is (8/5, -6/5, 0) Cross 1, 1, 3, 5 2, 1, 2, 1, 1 Is a dirrection of the line Math1502Q2Ans.nb 3 Math 1502 Quiz #2 Oct 8 Tom Morley 8:00 am. Put name and TAs name on each page. Do not Staple. Name: ______________________________________ TA: Problem 3: (10 Points) Describe solution exists, solution doesn ' t exist, solution unique, etc of the following system. Note that this will depend on the parameters a and b. x x 2x y ay 2y z 2z z b 1 1 A ns ax y 2z x 2y 4z 2x z 4 Clear a, b eqns x y z x y b, x z ay b, 2z x ay 1, 2 x 2z 2y z 1, 2 x 1 2y z 1 2 b Reduce eqns, b 1 2 && a a x, y , z 1 x && z 1 a 4b ab && y 3 1a 1 && y 5 1 1 3 b 3 x && z 1 1 3 2b 0 && x If a If b If a 1, then unique solution 2 and a 1, then infinitely many solutions 1 and b 2 then no solutions. ...
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More Sample problems - 2 Math1502Q2Ans.nb Math 1502 Problem...

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