0. Given the vectors
$v_1 = (1, 1, -1)$, $v_2 = (-1, -2, 4)$, $v_3 = (-2, a, 5)$, $v_4 = (3, -2, -2)$
in $R^3$
(a) For what values of $a$ are the vectors linearly dependent?
(b) Find the value(s) of $a$ such that the span of $v_1, v_2, v_3, v_4$ has dimension 3.
(c) Find the value(s) of $a$ such that the span of $v_1, v_2, v_3, v_4$ has dimension 2.