Let V(F) be a finite-dimensional vector space and T: V → V be a linear transformation. Let R(T) denote the range of T and N(T) denote the null space of T. If rank(T) = rank(T2), then which of the following statements are correct? (A) N(T) = N(T2) (B) N(T) ∩ R(T) = {0} (C) R(T) = R(T2)

Let A ∈ &mathbb;R7×7. Define S = { λ ∈ &mathbb;R : det(A - λI) = det(λI - A) }. Then which of the following is correct?

Consider the matrix A = 11α1-10β21-1γ0. Which of the following statements is correct?

Let f : P3(&mathbb;R) → P3(&mathbb;R) be a linear operator such that f(1) = 1 + 2x + 3x2, f(x) = x + 2x2, f(x2) = x2, and f(x3) = x3. Which of the following statements is NOT true?