7. For each of the following statements, determine whether it is True or False and explain your reasoning. (a) (3 points) Let A be an m x n matrix and suppose that the entries in each row of A add up to 0. Then A is invertible. (b) (3 points) Let 7, y, z be vectors in a vector space R" then span {I, y, 2} = span {I + y, 7 + 7 + 2,Ity - 2}(c) (3 points) If A is an n x n matrix with n distinct eigenvalues, then A is invertible. I2 (d) (3 points) Let A = wow ... WOO NN... NNO 30.000 and b - If A = b, ... then In = 1.(e) (3 points) Let A be an m x n matrix with m # n. A consistent system Ar - b has a unique solution if and only if AT - 0 has only the trivial solution. (f) (3 points) Let V be the set of pairs (r, y) with r, y E R where vector addition is defined by: (1, y1) + (12, y2) = (21 + 12, 1) ad scalar multiplication by a E R is defined by: a(x, y) = (ax, ay) Then V is a vector space