quiz2_S04_solutions

quiz2_S04_solutions - MATH 202 QUIZ 2 Due Friday April 16...

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Unformatted text preview: 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 1. (8 pts) For the matrix A = 4 1- 2 1- 2 1 (a) Compute the characteristic polynomial of A . (b) Find the eigenvalues of A . det( A- λI ) = det 4- λ 1- 2 1- λ- 2 1- λ and we expand on the second column to get (1- λ ) det " 4- λ 1- 2 1- λ # = (1- λ )[(4- λ )(1- λ ) + 2] = (1- λ )( λ- 2)( λ- 3) . So the characteristic polynomial is ( λ- 1)( λ- 2)( λ- 3) = 0 . and the eigenvalues are λ = 1 , 2 , 3. 2. (5 pts) Find the line y = mx + b that best fits the data points (- 1 , 0), (0 , 1),(1 , 2) and (2 , 4). The data points give us the (inconsistent) matrix equation - 1 1 1 1 1 2 1 " m b # = 1 2 4 Multiply through on the left by the transpose "- 1 1 2 1 1 1 1 # to get the normal equation " 6 2 2 4 # " m b # * = " 10 7 # Then solve the system...
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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_solutions - MATH 202 QUIZ 2 Due Friday April 16...

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