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**Unformatted text preview: **rsing the 0
1 direction. This ﬂips everything upside-down.
HW: We have eigenvalues λ = 1, −1, and representative eigenvectors are
3
1
direction, vectors are being held ﬁxed, and in the
−5
−2
reversed. It’s not exactly a mirror image, though. Can you picture it? that in the 2) We have eigenvalues λ = 1, 2 and representative eigenvectors
ﬁxed in the 3
−1 3
−1 and direction, and being stretched by a factor of 2 in the 3
−5 and 1
−2 . This means direction the vectors are being 2
. Things are being held
−1
2
direction.
−1 3) The vectors are being rotated by 90◦ in the clockwise direction.
4) No. No vector is being mapped to a scalar multiple image of itself. All vectors map to a vector pointing
in a diﬀerent direction.
5) You would solve
to rotations. −λ
−1 1
−λ = λ2 +1 = 0. This has no real solutions. Imaginary solutions will correspond...

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