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Unformatted text preview: M340L Fall 2010: Exam 1 Practice Problems Problem 1. Consider the system of 3 linear equations in 3 variables: 5 x 1 3 x 2 + 8 x 3 = 4 x 1 + x 2 = 0 6 x 1 2 x 2 + 8 x 3 = 4 a) Express this system as a matrix equation of the form A x = b . What are A and b ? How is x related to the variables x 1 ,x 2 ,x 3 ? b) What is the solution set S 1 of this system? Describe it in parametric form. (Recall that parametric form means giving a formula for the solutions such as x = t v + p where t is arbitrary, or x = t 1 v 1 + t 2 v 2 + p where t 1 and t 2 are arbitrary.) c) What is the solution set S 2 of the system A x = ? Describe it in parametric form. d) Describe S 1 and S 2 geometrically as subsets of R 3 : is each one an empty set, a point, a line, a plane, or a threedimensional space? How are they related geometrically to one another? Problem 2. Consider the matrices A = 1 3 4 2 1 , B = 1 0 3 2 4 0 , C = 4 2 3 0 ....
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This note was uploaded on 10/19/2010 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas at Austin.
 Spring '08
 PAVLOVIC
 Linear Equations, Equations

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