Determine which of the following subsets of R n. with n ge 1. are in fact subspaces. Justify your answers. {x R n : xi ge 0 i = 1. ,n}; {x R n : X 1 = 0}; {x R n : x1x2 = 0 n ge 2}: {x R n : x1 + + x n=0}: {x R n : x1 + + x n = 1}; {x R n : Ax = b. A 0, b 0}. Determine which of the following subsets of F n, n, with n ge 1, are in fact subspaces. Justify your answers. {A F n, n : A = A T}; {A F n, n : A invertible}; {A F n, n : A not invertible}; {A F n, n : A upper-triangular}; {A F n, n : A2 = A}: {A F n, n : tr (A) = 0}. Given a matrix X F n, n, define {A F n, n : [A. X] = 0}