ﬁnd the eigenvalues of A by ﬁrst generating the characteristic polynomial for A using poly and then using roots to ﬁnd the roots of the resulting polynomial.

For the matrix given in Problem 2.12, useeig to ﬁnd the eigenvalues. Then ﬁnd the eigenvalues of A by ﬁrst generating the characteristic polynomial for A using poly and then using roots to ﬁnd the roots of the resulting polynomial. Use sort to compare the results of the two approaches. What conclusions do you draw from these results? For the matrix given in Problem 2.14, taking n=10, show that the trace is equal to the sum of the eigenvalues and the determinant is equal to the product of the eigenvalues.Usethe MATLAB functions det, trace, and eig.

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