\f(a) (6 marks) Let L :2 R3 > R3 be a linear map such that L(-v1) = 1:1, L(-v2) = 1:2, L(-v3] = 1:4 and L(-v.1) = 1:3. \"Trite down the matrix of L in the standard frame. Give a geometrical description of L. (b) (6 marks) Let ft! := R3 > R3 be a linear map with the matrix 1/2 1/2 1N5 1/2 1/2 1/\\/ 1N5 1/\\/ 0 in the standard frame. Is if a symmetry of the tetrahedron? If yes, how does it permute the vertices? (c) (8 marks) Prove that L 0 Mr is an orthogonal map with respect to the standard dot product. Give a geometrical description to L 0 1M