Let S be the tetrahedron in R3 with vertices at the vectors 0, e1, e2, and e3,

Question:

Let S be the tetrahedron in R3 with vertices at the vectors 0, e1, e2, and e3, and let S' be the tetrahedron with vertices at vectors 0, v1, v2, and v3. See the figure

a. Describe a linear transformation that maps S onto S'.
b. Find a formula for the volume of the tetrahedron S' using the fact that
{Volume of S} = (1/3) {area of base} ( {height}