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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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This note was uploaded on 10/12/2011 for the course MATH 464 taught by Professor Dougbullock during the Fall '08 term at Boise State.
 Fall '08
 DougBullock
 Math, Eigenvectors, Vectors

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