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**HallsofIvy** What happened to the last row? But what you have done is correct, so far. If you were to complete the row reduction you would have, as reduced echelon form,

$\displaystyle \left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\\ 0 & 0 & 0\end{array}\right]$

so that your basis vectors are <1, 0 , 0>, <0, 1, 0>, and <0, 0, 1>, the standard basis for $\displaystyle R^3$. That is because this matrix maps $\displaystyle R^4$ into $\displaystyle R^3$ and its null space has dimension 1 so its image is all of $\displaystyle R^3$.