Question: Please help me to answer this question 12.2.24. V is a vector space of dimension three, and T: V -> V is a linear transformation.

Please help me to answer this question

12.2.24. V is a vector space of dimension three, and T: V -> V is a linear transformation. We know that 73 = 0 is the zero transformation, and T2 # 0. Let v E V have the property that T2(v) * 0, and let B = {v, T(v), T2(v) }. (a) Can B be linearly dependent? Either give an example where it is depen- dent, or prove that it is always linearly independent. For the rest of the problem assume that B is a basis for V. (b) Find [T]B,B, the matrix of T with respect to B. (c) Is T diagonalizable? Why

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