 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-1/section-b/8/a/iii/solution

True. Applying the matrices in order gives

A B x = A (b x) = ab x

ab .

This conclusion only uses the shared eigenvector; it does not require

A

and

B

to commute on other vectors.

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