A 2x2 matrix multiplies with the corners of a unit (2-D) square to produce a quadrilateral with area of its determinant. What analogous process does the 3x3 matrix perform?

Question

cruffo · Answer

Volume?

anonymous · Answer

On a unit cube, I suppose. Thanks for that, brain failure on my part.

cruffo · Answer

Well, you don't know how the 3x3 will scale the unit square.  I'm thinking it will be the volume of a parallelepiped.

cruffo · Answer

Sory, not unit square, I ment unit cube!

anonymous · Answer

Yes, assumedly.

anonymous · Answer

http://images1.wikia.nocookie.net/__cb20100410052545/uncyclopedia/images/c/c3/Determinant_parallelepiped.png Seems almost exactly the same as with 2 dimensions.

cruffo · Answer

Cool!

cruffo · Answer

Right the 3x3 will transform the cube - skewing and scaling it.  So it may not be a "cube" anymore.

anonymous · Answer

Just as the scales square isn't a square any more

anonymous · Answer

Thanks!

cruffo · Answer

Cheers!