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# ws13 - Math 464 Worksheet 13 This worksheet is an exercise...

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Unformatted text preview: Math 464, Worksheet 13 This worksheet is an exercise in locating points in the plane. Each vector is a point. Each point has a location. Each location has two descriptions: one in Cartesian coordinates and one in terms of eigenvectors. Complete the following table of Cartesian and eigenvector descriptions. Refer to Worksheets 11 and 12 as needed. Vector Cartesian description Steps along v1 Steps along v2 1 v1 1 M v1 v2 M v2 v2 − v1 M (v2 − v1 ) −4 −3 3v1 − 3v2 M (3v1 − 3v2 ) w Mw i Mi M 10 i Answers are on the next page. For kicks, you can also spend some time multiplying P −1 times each entry in the Cartesian column. Compare these answers to the eigenvector descriptions. 1 Answers Vector v1 Cartesian description 1 1 Steps along v1 Steps along v2 1 0 M v1 4 4 4 0 v2 1 2 0 1 M v2 −3 −6 0 −3 v2 − v1 0 1 −1 1 M (v2 − v1 ) −7 −10 −4 −3 3v1 − 3v2 0 −3 3 −3 M (3v1 − 3v2 ) 21 30 12 9 w −2 2 −6 4 Mw −36 −48 −24 −12 i 1 0 2 −1 Mi 11 14 8 3 M 10 i 2038103 1979054 2 · 410 −1 · (−3)10 2 ...
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