Let S be the tetrahedron in $R^3$ with vertices at the vectors $0,e_1, e_2, e_3$ and let $S^l$ be the tetrahedron with vertices at vectors $0, v_1, v_2, v_3$
a) Describe a linear transformation that maps $S$ onto $S^l$
b) Find a formula for the volume of the tetrahedron $S^l$ using the fact that
{volume of S}=(1/3){area of base}{height}
I tried doing b) by myself and here is what i came up with, i need someone to check my work...
1) (1/3){area of base}{height}
2) (1/3){1/2 h * b}{$v_3$ - 0}
3) (h*b($v_3$ - 0))/6
4) (($v_2$ - 0)($v_1$ - 0)($v_3$ - 0))/6
5) ($v_2$ * $v_1$ * $v_3$)/6
did i make any errors?