Answer
$A=\left[\begin{array}{ l l l }2&1&1\\2&2&0\\2&0&3\end{array}\right]$
Work Step by Step
Let$A=\left[\begin{array}{ l l l }2&1&1\\2&2&0\\2&0&3\end{array}\right]$be matrix is not in echelon matrix.
Reduce matrix to reduce echelon form:
$\left[\begin{array}{ l l l }2&1&1\\2&2&0\\2&0&3\end{array}\right]$
multiply first row' with - 1and add to sccond and third
$\sim \left[\begin{array}{ c c c }2&1&1\\0&1&-1\\0&-1&2\end{array}\right]$
add second row to third
$\sim \left[\begin{array}{ c c cc}2&1&1\\0&1&-1\\0&0&1\end{array}\right]$
divide first row with 2
$\sim \left[\begin{array}{ c c c }1&1/2&1/2\\0&1&-1\\0&0&1\end{array}\right]$
add third row to second and multiply third row with-1/2 and add to first
$\sim \left[\begin{array}{ c c c }1&1/2&0\\0&1&0\\0&0&1\end{array}\right]$
multiply second row with -1/2and add to first
$\sim \left[\begin{array}{ c c c }1&0&0\\0&1&0\\0&0&1\end{array}\right]$
Since there are 3 pivot columns they span $R^3$.
$A=\left[\begin{array}{ l l l }2&1&1\\2&2&0\\2&0&3\end{array}\right]$
