rank-nullity-theorem

Let A be any n × m matrix, where m > n. Which of the following statements is/are TRUE about the system of linear equations Ax = 0 ?

Let A be any n x m matrix, where m > n . Which of the following statements is/are TRUE about the system of linear equations Ax = 0 ?

Suppose that P is a 4 × 5 matrix such that every solution of the equation P x = 0 is a scalar multiple of [2 5 4 3 1] T ​. The rank of P is _________