1. Find the transition matrix from the basis to the basis
2. Let A and B be two linear operators on given by the formulas
Put . Find the matrices of A, B, and C with respect to the standard basis.
3. The standard basis for the linear space of 2 x 2 matrices consists of four matrices
4. A linear operator has a matrix with respect to the standard basis . Find the matrices of this operator with respect to the bases
5. Prove that the composition of two rotations by angles and in is the rotation by the angle .