Simple Yes or No Will Do Eigenvectors

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SUMMARY

The discussion centers on a homework problem regarding the eigenvectors of 3x3 matrices. The user questions the validity of the problem, asserting that the provided vectors <1, 1> and <1, 2> cannot serve as eigenvectors for a 3x3 matrix due to their dimensionality. The consensus is that eigenvectors must match the matrix's dimensionality, thus indicating a potential error in the problem statement. The conclusion is that the problem is indeed flawed as stated.

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  • Knowledge of matrix dimensions and their implications
  • Familiarity with 3x3 matrices and their properties
  • Basic concepts of vector spaces
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Simple Yes or No Will Do... Eigenvectors

Homework Statement



I think my prof made a mistake when writing this problem:

Find a basis of the space V of all 3 x 3 matrices A for which the vectors <1, 1> and <1, 2> are eigenvectors and thus determine the dimensions of V.

Is this problem possible? Wouldn't the matrices have to be 2 x 2 given the vectors?
 
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It sounds like a mistake; the eigenvectors of a 3x3 matrix would each be of dimension 3.
 

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