rank

Two vectors $[2 \ 1 \ 0 \ 3]^T$ and $[1 \ 0 \ 1 \ 2]^T$ belong to the null space of a $4 \times 4$ matrix of rank 2. Which one of the following vectors also belongs to the null spa...

Let y be a non-zero vector of size 2022 × 1. Which of the following statement(s) is/are TRUE?

Let y be a non-zero vector of size 2022 $$\times$$ 1. Which of the following statements is/are TRUE?

The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3 \\ 3 & 4 & 2 & 5 \\ 5 & 6 & 2 & 7 \\ 7 & 8 & 2 & 9 \end{bmatrix}$ is

The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0 \\ 0 & 2 & 0 & 1 \\ -5 & 0 & 5 & 0 \\ 0 & 1 & 0 & 2 \end{bmatrix}$ is

The rank of the following matrix is $\begin{pmatrix} 1 & 1 & 0 & -2 \ 2 & 0 & 2 & 2 \ 4 & 1 & 3 & 1 \end{pmatrix}$

Let $$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$ with $$n \ge 3$$ and $${{a_{ij}} = i.j.}$$ The rank of $$A$$ is :

The rank of the matrix $$\left[ {\matrix{ 6 & 0 & 4 & 4 \cr { - 2} & {14} & 8 & {18} \cr {14} & { - 14} & 0 & { - 10} \cr } } \right]$$ is