Demonstrates that every poly­nomial is (plus or minus) the characteristic polynomial of its own companion matrix. Therefore, the roots of a poly­nomial pare th e eigenvalues of C(p). Hence, we can use the methods of this section to approximate the roots of any polynomial when exact results are not readily available. Apply the shifted inverse power method to the companion matrix C ( p) of p to approximate the root of p closest to a to three decimal places. p(x) = x3 -5x2 + x + l, α= 5

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