Rank of Matrix/Examples/Arbitrary Matrix 2

Examples of Rank of Matrix
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 $2$.

Proof
From Matrix is Row Equivalent to Echelon Matrix: Arbitrary Matrix $2$, the echelon form $\mathbf E$ of $\mathbf A$ is:
 * $\mathbf E = \begin {bmatrix} 1 & 1 & 1 & 1 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 \end {bmatrix}$

There are $2$ non-zero rows in $\mathbf E$.

The result follows by definition of rank of matrix.