EXERCISE 4. (i) Let W be the plane in $\mathbb{R}^3$ defined by the equation
$4x + y - 3z = 0$.
Find a basis $B$ for this subspace of $\mathbb{R}^3$.
(ii) Show that the vector $v = (2, 1, 3)$ lies in $W$ and express it in terms of the basis $B$.
(iii) If $(w)_B = (-2, 4)$ then what is $(w)_S$ (where $S$ is the standard basis of $\mathbb{R}^3$)?