Consider the regular tetrahedron in the accompanying sketch whose center is at the
Chapter 3, Problem 74(choose chapter or problem)
Consider the regular tetrahedron in the accompanying sketch whose center is at the origin. Let 0o, 0i, 02, 03 be the position vectors of the four vertices of the tetrahedron:00 = OPq,..., 03 = OP3.a. Find the sum 0o + 0i + 02 + 03b. Find the coordinate vector of 0o with respect to the basis 0i, 02, 03.c. Let T be the linear transformation with T(vo) = 03, T(v3) = 0i, and T(0i) = 0q. What is T(v2)? Describe the transformation T geometrically (as a reflection, rotation, projection, or whatever). Find the matrix B of T with respect to the basis 01, 02, 03. What is Z?3? Explain.
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