Problem 6. {2.4mm Consider the regular tetrahedron sketched at right1 whose center is at the origin. Let T from R3 to R3 be the Let L from R3 to R3 be the rotation about the axis reection about the plane through points [I and F: that through the points (I, Pu. and transforms F1 into P3. Find 1 P3. Find the images ofthe the images of the four _ four corners of the tetrahedron comers ofthe tetrahedron under this transformation. under this transformation. Describe the transformations in parts {a} through {c} geometrically. Ff: > Ff: '> a. T'] b. L'] c. T3 = T9?" [the composite of Twith itself} P _} P _} d. Find the images ofthe four corners under the transformations To L Fl _} Fl _} and Lu T. Are the two transformations the same? 3 e. Find the images of the four corners under the transformation Ln Tu L. P3 _> P; _> Describe this transformation geometrically. Problem 7. (2.4/81) Find the matrices of the transformations 7 and Z defined in Problem 6 above