Identity Matrix from Upper Triangular Matrix/Examples

Examples of Use of Identity Matrix from Upper Triangular Matrix

Arbitrary Matrix 1

Let $\mathbf A$ be the matrix defined as:

$\mathbf A = \begin {bmatrix}

1 & 1 & 1 & 1 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 4 \\ \end {bmatrix}$

is row equivalent to the reduced echelon matrix:

$\mathbf E = \begin {bmatrix}

1 & 0 & 0 & -\dfrac 1 2 \\ 0 & 1 & 0 & \dfrac 1 6 \\ 0 & 0 & 1 & \dfrac 4 3 \\ \end {bmatrix}$