quiz2_S04 - 1 , ~v 2 = 1 2 3 4 , ~v 3 = 1 3-1 1 5. (12 pts)...

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Name Class Time MATH 202 - QUIZ # 2 Due Friday, April 16 at 2PM Covers 5.3, 5.4, Chapter 6, 7.1 and 7.2 of the text Time: 60 minutes 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 the Wednesday 2PM deadline. 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. (8 pts) For the matrix A = 4 0 1 - 2 1 0 - 2 0 1 (a) Compute the characteristic polynomial of A . (b) Find the eigenvalues of A .
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2. (5 pts) Find the line y = mx + b that best fts the data points ( - 1 , 0), (0 , 1),(1 , 2) and (2 , 4).
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3. (8pts) Let V be the subspace of R 4 spanned by ~v 1 = 1 0 - 1 1 and ~v 2 = 0 1 1 0 Find the vector in V that is closest to ~ b = 1 4 1 0
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4. (8pts) Find the volume of the 3-parallelopiped in R 4 with edges ~v 1 =
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Unformatted text preview: 1 , ~v 2 = 1 2 3 4 , ~v 3 = 1 3-1 1 5. (12 pts) (a) Find a 2 × 2 matrix A whose eigenvalues are λ 1 = 1 2 and λ 2 = 3 2 with corresponding eigenvectors ~v 1 = " 4 2 # and ~v 2 = " 2-4 # . (b) Sketch the phaseportrait for the dynamical system ~x ( t + 1) = A~x ( t ). (c) If D is the unit disk and if T ( ~x ) = A~x then what is the area of T ( D )? 6. (9 pts) (a) A 4 × 4 matrix A has eigenvalues-1 , 1 , 3 , 5. What is the determinant of A-1 ? (b) Given that λ is an eigenvalue for the 4 × 4 matrix A , use this to Fnd an eigenvalue for the matrix A 2-A . (c) If A and B are n × n orthogonal matrices, then show that AB is also an orthogonal 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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quiz2_S04 - 1 , ~v 2 = 1 2 3 4 , ~v 3 = 1 3-1 1 5. (12 pts)...

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