38. If a linear transformation T: R³→R³ is defined by:T(x, y, z) = (3x+2y, -2x+3y, 5z), which of the following statement is incorrect?(A) The basis of the kernel (null space) of T is {0}.(B) T is one to one.(C) T is onto.(D) T is invertible.(E) T is not diagonalizable over the real field.

39. Which of the following statements is true?(A) Let S = {v₁, v₂, ..., vk} be a set of vectors in Rⁿ. Let A ∈ Mmxn(R). If S is linearly independent, then S' = {Av₁, Av₂, ..., Avk} is also linearly independent(B) Let S be a set of vectors in a finite-dimensional vector space V. Then, span(S) is the intersection of all subspaces of V that contains S(C) Assume that S = {v₁, v₂, ..., vn} is a subset of a vector space V. If S is linearly dependent, then there exists a proper subset of S that is a basis for V(D) The basis of any vector space is unique(E) Assume that S = {v₁, v₂, ..., vn} is a subset of a vector space V. If S is linearly independent, then there exists a proper subset of S that is a basis for V

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