5. Determine whether the following statements are true or false. Justify your response.

(a) There exist homogeneous systems of linear equations which are not consistent.

(b) If for each b in Rm the equation Ax = b has a solution, then the columns of A

span Rm

(c) The columns of any 4 × 5 matrix are linearly dependent.

(d) Let A be an m x n matrix, u and v be vectors in R", and c and d be scalars. If u

and v are both solutions of the homogeneous system Ax = 0, then w = cu + dv

is also a solution of Ax = 0.