We have $\vec{u}$ , $\vec{v}$ , $\vec{w}$ are three vectors of vector space
We have $\vec{a} , \vec{b} , \vec{c}$ such as:
$$\vec{a} = 2*\vec{u} + \vec{v} + \vec{w} $$ $$\vec{b} = \vec{u} + 2*\vec{v} + \vec{w}$$ $$\vec{c} = \vec{u} + \vec{v} + 2*\vec{w}$$
How can we write $\vec{u} , \vec{v} , \vec{w}$ in terms of $\vec{a} , \vec{b} , \vec{c}$?
$\vec a+\vec b+\vec c=4\left(\vec u+\vec v+\vec w\right)$ and$$\vec a=\vec u+\vec u+\vec v+\vec w=\vec u+\frac14\left(\vec a+\vec b+\vec c\right).$$Therefore,$$\vec u=\frac34\vec a-\frac14\vec b-\frac14\vec c.$$The other vectors are similar.