Rank of Matrix/Examples

Examples of Rank of Matrix

Arbitrary Matrix $1$

Let $\mathbf A = \begin {bmatrix} 0 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \\ \end {bmatrix}$

The rank of $\mathbf A$ is $3$.

Arbitrary Matrix $2$

Let $\mathbf A = \begin {bmatrix} 1 & 1 & 1 & 1 \\ 2 & 3 & 4 & 5 \\ 3 & 4 & 5 & 6 \end {bmatrix}$

The rank of $\mathbf A$ is $2$.

Arbitrary Matrix $3$

Let $\mathbf A = \begin {bmatrix} 1 & 2 & 3 & 5 \\ 1 & 2 & 3 & 4 \\ 0 & 0 & 1 & 1 \end {bmatrix}$

The rank of $\mathbf A$ is $3$.

Arbitrary Matrix $4$

Let $\mathbf A = \begin {bmatrix} 1 & 1 & 2 & 3 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 3 & 3 \end {bmatrix}$

The rank of $\mathbf A$ is $2$.

Arbitrary Matrix $5$

Let $\mathbf A = \begin {bmatrix} -1 & 0 & 1 & 2 & 3 \\ 0 & 1 & 2 & 3 & 4 \\ -1 & -2 & -3 & -4 & -5 \end {bmatrix}$

The rank of $\mathbf A$ is $2$.