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Let S be the tetrahedron in R3 with vertices at X3 the vectors 0 0...

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Algebra

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Let S be the tetrahedron in R3 with vertices at X3 the vectors 0 0 02 and e3 and let S be the tetrahedron with vertices at vectors 0 V V and v3 See the figures to the right Complete parts a and b below a Describe a linear transformation that maps S onto S If T is a linear transformation that maps S onto S then the standard matrix for T written in terms of V V and V3 is A 1 b Find a formula for the volume of the tetrahedron S using the fact that volume of S 3 A 1 O C 1 2 det v det V V V3 det V V V3 area of base height OB det V V V3 V2 OD 1 det V V V3

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