Subject GRE-Style: Eigenvalue Problem

GRE Math Subject · Axiom Academy

EXAMPLE Subject GRE-Style: Eigenvalue Problem A complete worked example with step-by-step solution Question: Which of the following is an eigenvector of with eigenvalue 6? Before looking at the solution, which answer do you think is correct? Verify that 6 is an eigenvalue First, verify that is indeed an eigenvalue by checking that : Good! Now we need to find which vector satisfies . Why this works: We computed , confirming that this vector is an eigenvector with eigenvalue 6. Key lesson: To find eigenvectors, you can either solve the system explicitly, or test the given options by computing and checking if it equals . On the GRE, testing options is often faster!

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