quiz1_F07 - r and s is the corresponding transformation T...

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Name Class Time MATH 202 - QUIZ # 1 Wednesday, October 10, 2007 Covers Chapter 1 and Chapter 2 of the text Please show all work. Books, notes, calculators, are not permitted on this quiz. As part of your obligations under the Honor Code, do not discuss this quiz with anyone until after 1:30 today. WRITE OUT AND SIGN THE PLEDGE: I pledge my honor that I have not violated the Honor Code during this examination.
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1. (12 points) Find all solutions to the linear system 2 x + y + z = 7 x + 3 y - 2 z = 1 8 x + 9 y - z = 23 Interpret the result geometrically.
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2. (12 points) Let T : R 2 R 3 be a linear transformation such that T p 2 1 P = 1 3 6 and T p 5 3 P = 10 15 21 Find the matrix of T .
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3. (12 points) For all possible choices of the parameters r and s consider the linear transformation from R 3 to R 3 de±ned by: T x y z = 1 0 r - 1 - r s 2 - 1 r r 2 - s 2 x y z (a) For what choices of the parameters
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Unformatted text preview: r and s is the corresponding transformation T in-vertible? (b) For which values of r and s will the matrix have rank 2? (c) For which values of r and s will the matrix have rank 1? 4. (12 points) True or False? Briefy explain your answers. (a) There exists a 7 4 matrix A o rank 4 so that A 1 2 3 4 = . (b) There is a system o 3 linear equations in 5 variables with exactly one solution. (c) Let L be any line through the origin in R 2 . I P is the matrix o projection onto L and R is the matrix o refection across L then PR = RP . (d) Suppose that A is a 2 3 matrix, B is a 3 2 matrix and AB = I 2 . Then BA is a 3 3 invertible matrix....
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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_F07 - r and s is the corresponding transformation T...

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