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Chapter 6: Q33E (page 289)

For which angle(s) 胃 can you find three distinct unit vectors in鈩�2 such that the angle between any two of them is胃 ? Draw a sketch.

Short Answer

Expert verified

The Angle is 胃=1200

Step by step solution

01

The Eigenvector

  • An eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by no more than a scalar factor when that linear transformation is applied to it.
  • The factor by which the eigenvector is scaled is represented by the associated eigenvalue, which is frequently denoted by lambda.
02

Determine the angle

The angle must add up to2蟺rad=3600(measure of one complete cycle), and the angle for which we can find three distinct eigenvectors in鈩�2is given by

胃=3603=1200The sketch is shown below.

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Most popular questions from this chapter

Find the determinants of the linear transformations in Exercises 17 through 28.

23.L(A)=ATfrom鈩�n脳nto鈩�n脳n

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