Consider the regular tetrahedron in the accompanying sketch

Consider the regular tetrahedron in the accompanying sketch whose center is at the origin. Let vo, v1, v2, v3 be the position vectors of the four vertices of the tetrahedron 0..., V3OP a. Find the sum vo + vi + v2 +V3. b. Find the coordinate vector of VO with respect to the basis u 1 , U2, U3. c. Let T be the linear transformation with T (vo) 70-3) = UI , and T(Ü, ) = v0. What is T(v2)? De- scribe the transformation T geometrically (as a re- flection, rotation, projection, or whatever). Find the matrix B of T with respect to the basis V1, v2, v3 What is B3? Explain 0

Solution

a) v0+ v1+ v2+ v3

addition of all the given matrices= 0

0

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