http://people.tamu.edu/~mrs6817/8.2.18.html

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Little or no calculation is needed ot answer the following questions.

a) Which matrix can be diagonalized by an orthogonal matrix?

Matrix B, because it is symmetric can be.

b) Which matrix can be diagonalized, but only by a nonorthogonal matrix?

Matrix A, although not symmetric still has unique eigenvalues, so it can be diagonalized.

c) Which matrix can't be diagonalized?

Matrix C's eigenvalues are the same, so it cannot be diagonalized.