(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

So there's a linear transformation T: ℝ^{3}→ ℝ^{4}, standard matrix A that satisfies

det(A e1) = 5, det (A e2) = 4, det (A e3) = 5 and det (A e4) = 5

If S is the unit sphere, find the 3-dimensional volume of T(S).

2. Relevant equations

Volume of sphere = 4/3 * pi * r^3

Volume based on determinants = det(A^{T}A)

3. The attempt at a solution

I know the determinant of a matrix can be seen as the scaling factor for the volume change of a transformation. So the answer will be 4/3 * pi * (something). The (something) will probably be some kind of combination of the determinants above (5,4,5,5), but I have no clue how to find its value. I have spent hours on this question, it's driving me crazy. Help!

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# Homework Help: Volume of a sphere under a linear transformation R3->R4.

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