Determinants as Area or Volume

[Lonely Lemon]

Homework Statement

If S is a parallelepiped determined by v1=(1, 1, 0) and v2= (3, 2, 1) and v3=(6, 1, 2) and T: R3--> R3 by T(x)=Ax, find the volume of T(S)

Homework Equations

{volume of T(S)}=|det A|.{volume of S}

The Attempt at a Solution

A is [v1 v2 v3] and the |A| = 9 by my calculations. I thought this was the volume, but the answer to the questions is given as 24. Please help!

 

[vela]

So the vectors define both the solid S and the mapping A? Just want to make sure you've described the problem as assigned.

 

[Lonely Lemon]

I assume so, that's the problem posed word for word. T: R3-->R3 is the linear transformation determined by a 3x3 matrix A, and S is the a parallelepiped in R3, so the vectors define both?

 

[vela]

If that's true, then shouldn't the volume of T(S) be a perfect square? By the way, I get det A=3, so you might want to recheck your calculations.