Reduce a set of vectors of $\mathbb{R}^3$ to a basis $V_1 =(1,0,0); V_2=(0,1,-1); V_3= (0,4,-3); V_4=(0,2,0)$ reduce this to obtain a basis for $\mathbb{R}^3$ .        I obtained a matrix as follows and then obtained its row echelon form, but then i cannot understand how I obtain basis from that matrix. 
$$\begin{bmatrix} 1 &0 &0 &0\\ 0 &1 &4& 2\\ 0 &-1 & -3& 0\end{bmatrix}$$ and its row echelon form is $$\begin{bmatrix} 1 & 0 & 0 &  0\\ 0 &1 &4 & 2\\ 0 & 0& 1 &2 \end{bmatrix}$$

Since $v_1, v_2, v_3$ are linearly independent, and we know that $\mathbb{R}$ has the dimension 3, the vectors $v_1, v_2, v_3$ forms a basis for $\mathbb{R}$.
