5 determine whether the following statements are true or false justify

Question

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.