Practice question · Multiple choice
A transformation stretches the plane. Vector satisfies . What is geometrically special about ’s direction?
Hints
- points the same way as , only longer.
- Most vectors get knocked off their line by a transformation. Eigenvectors are the stubborn ones that stay on theirs.
Show the answer
B. The transformation keeps that direction fixed, stretching 3×
Why
Eigenvectors mark the invariant axes of a transformation, the directions it cannot turn, only rescale (by the eigenvalue). Finding them reveals a transformation’s skeleton: along those axes, matrix action reduces to simple multiplication.
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