Discussion
A student computes eigenvalues 3 and 5 for a matrix of trace 9. The error is evident because the eigenvalues should
Answer: B
Correct answer: sum to the trace
The trace equals the sum of the eigenvalues and the determinant equals their product, both following from the characteristic polynomial. Here \( 3+5 = 8 \neq 9 \), so at least one eigenvalue is wrong. It is the quickest check available on an eigenvalue calculation, and it costs nothing to make.
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