Practice question · Sort into groups
Let A = [3, 0 ; 0, -1], written as rows separated by a semicolon. Sort each vector by whether it is an eigenvector of A.
Groups: Eigenvector of A · Not an eigenvector of A
- (2, 3)
- (1, 0)
- (0, 0)
- (0, -5)
- (1, 1)
- (0, 1)
Hints
- Multiply each vector by A and ask whether the result is a multiple of the original.
- One item is excluded by the definition itself rather than by a computation.
Show the answer
Eigenvector of A: (1, 0), (0, 1), (0, -5)
Not an eigenvector of A: (1, 1), (2, 3), (0, 0)
Why
A multiplies the first coordinate by 3 and the second by -1, so (1,1) goes to (3,-1) and (2,3) to (6,-3), neither a multiple of the original. The zero vector satisfies A0 = lambda 0 for EVERY lambda, so it is excluded by definition, an eigenvector must be nonzero.
Practise Eigenvalues and Eigenvectors
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