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quiz2_F07

# quiz2_F07 - R 3 with edges v 1 v 2 v 3 has volume 6 then...

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Name Class Time MATH 202 - QUIZ # 2 Wednesday, December 5, 2007 Covers 5.3-5.4, 6.1-6.3, 7.1-7.3 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) Consider the matrix A = - 3 0 - 2 1 - 1 1 1 0 0 (a) Calculate all the eigenvalues of A . (b) For each eigenvalue of A , find a basis for the corresponding eigenspace. (c) For each eigenvalue of A indicate the algebraic and the geometric multiplicity.
2. (12 points)

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Unformatted text preview: R 3 with edges v 1 , v 2 , v 3 has volume 6, then what is the volume of the parallelepiped whose edges are v 1 + v 2 + 3 v 3 , 4 v 2 + 6 v 3 , and v 1 + 5 v 2 + 8 v 3 ? 3. (12 points) Find the quadratic polynomial of the form y = ax 2 + bx that best ±ts the four data points (-1 , 16), (0 , 8), (1 , 4) and (2 , 6). 4. (12 points) True or False? Justify your answers. (a) If A is a 3 × 2 matrix then 0 is always an eigenvalue of AA T . (b) If A and B are n × n matrices then tr AB = (tr A )(tr B ). (c) If A is a 2 × 2 matrix with characteristic equation λ 2-1 = 0 then A is an orthogonal matrix....
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quiz2_F07 - R 3 with edges v 1 v 2 v 3 has volume 6 then...

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