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Matrices and Determinants Questions and Answers

Answer: B

For a two by two matrix the pair of relations determines the roots completely, and for larger matrices they still provide two independent arithmetic checks. Both hold whatever the symmetry or the multiplicity of the eigenvalues.

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112.

Just one of these quantities is unchanged when a matrix is replaced by a similar matrix. Which?

Answer: C

Similar matrices represent the same map in different bases, so the characteristic polynomial and with it the eigenvalues, trace and determinant all survive. The entries, the triangular form and the basis itself all change.

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