Row Operation to Clear First Column of Matrix/Examples

Examples of Use of Row Operation to Clear First Column of Matrix

Let $\mathbf A$ be the matrix:

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

The matrix $\mathbf R$ corresponding to the row operation to clear the first column is:

$\mathbf R = \begin {pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & -1 & 1 \end {pmatrix}$

and the matrix $\mathbf B$ which results from the row operation $\mathbf R$ is:

$\mathbf B = \begin {pmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & -1 & 1 \end {pmatrix}$

Let $\mathbf A$ be the matrix:

$\mathbf A = \begin {pmatrix} 1 & 0 & 1 & 1 \\ -1 & 0 & 2 & 1 \\ -1 & 1 & 5 & 9 \end {pmatrix}$

The matrix $\mathbf R$ corresponding to the row operation to clear the first column is:

$\mathbf R = \begin {pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end {pmatrix}$

and the matrix $\mathbf B$ which results from the row operation $\mathbf R$ is:

$\mathbf B = \begin {pmatrix} 1 & 0 & 1 & 1 \\ 0 & 0 & 3 & 2 \\ 0 & 1 & 6 & 10 \end {pmatrix}$

Let $\mathbf A$ be the matrix:

$\mathbf A = \begin {pmatrix} 0 & 4 & 7 & 10 \\ 2 & 5 & 8 & 11 \\ 3 & 6 & 9 & 12 \end {pmatrix}$

The matrix $\mathbf R$ corresponding to the row operation to clear the first column is:

$\mathbf R = \begin {pmatrix} 0 & \dfrac 1 2 & 0 \\ 1 & 0 & 0 \\ 0 & -\dfrac 3 2 & 1 \end {pmatrix}$

and the matrix $\mathbf B$ which results from the row operation $\mathbf R$ is:

$\mathbf B = \begin {pmatrix} 1 & \dfrac 5 2 & 4 & \dfrac {11} 2 \\ 0 & 4 & 7 & 10 \\ 0 & -\dfrac 3 2 & -3 & -\dfrac 9 2 \end {pmatrix}$