Find basis for subspace given by $x_1/3=x_2/4=x_3/2$ Find a basis for the subspace W: $$
W = \left\{ \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3}\end{bmatrix} \in \mathbb{R}^3 \left| \dfrac{x_{1}}{3}=\dfrac{x_{2}}{4}=\dfrac{x_{3}}{2} \right.\right\}
$$
The two equation signs are really throwing me off. If it was a linear equation with one equation sign then I could easily find the basis by putting the equation in a matrix and solve for each variable but I cannot do this for this equation. Can anyone help me out? Thanks.

Once $x_1$ is fixed, we have $$x_2 = \frac{4}{3}x_1\text{ and }x_3 = \frac{2}{3}x_1$$ So all the elements in $W$ can be written as $$\left(x_1, \frac{4}{3}x_1, \frac{2}{3}x_1\right)$$ $W$ is 1 dimensional and one basis is $\left(1, \frac{4}{3}, \frac{2}{3}\right)$
