Please help me.

(10 pts] 1. (True or False) (1] There exists a 4 x 7 matrix A such that Ax = 0 has only trivial solution. (2) Every set of 3 nonzero vectors in R5 is linearly independent- (3) If A is a square matrix such that Ax = 0 has a nontrivial solution, then det(A) = 0. (4) For a 5 x 4 matrix A, if rank(A) = 3, then nullity(A) = 2. (5) If A is a 6 X 5 matrix such that rank(A) = 5, then Ax = 0 has only trivial solution