null-space

Consider $4 \times 4$ matrices with their elements from $\{0,1\}$. The number of such matrices with even number of 1 s in every row and every column is

Let $n>1$. Consider an $n \times n$ matrix $M$ with its elements from $\mathbb{R}$. Let the vector ( 0,1 , $0,0, \ldots, 0) \in \mathbb{R}^n$ be in the null space of $M$. Which of...

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 _________