Let $R^3$ be a vector space. Linear map $F$ will map base of $R^3$:
$u_1=(1,2,-1)^T$, $u_2=(1,-3,3)^T$, $u_3=(-1,-2,2)^T$
on vectors
$v_1=(-1,-3,5)^T$, $v_2=(2,5,-4)^T$, $v_3=(-2,-6,7)^T$.
How will the unit spheres volume change after mapping it with F?