1)a)What us the matrix, M that transforms i->u, j->v and k->w? and what is its determinant?
1)b)This matrix then transforms the cube with corners (0,0,0), (1,0,0),(0,1,0), (0,0,1), (1,0,1), (0,1,1), (1,1,0) and (1,1,1) what are the new corners and the new cubes volume?
Am I right in thinking that the matrix is [1,0,0;0,1,0;0,0,1] and that it will have no effect on the cube as this is the identity matrix?
2) a)By considering the effects on the unit vectors (1,0,0),(0,1,0), (0,0,1) show what transformations are represented by the matrices.
(0 = theta)
am I right in thinking that B is a rotation in the y axis with angle theta?
B) what what the effect of A then B on the vector [1,1,1] and also B followed by A?