Sentence:  A procedure for obtaining the <WSD>minimal polynomial</WSD> of the matrix T^i, without actually computing the powers of T is indicated in the solution to Problem 5.9. 
Meaning of the word marked with <WSD> tags:  For a given square matrix "M" over some field "K", the smallest-degree monic polynomial over "K" which, when applied to "M", yields the zero matrix.