LINEAR ALGEBRA (Math 211)
HW #15 (Due Fri. Dec. 1 )

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
A(x,y,z)=(2x,-2x+3y+2z,4x-y+5z)
B(x,y,z)=(-3x+z,2y+z,-y+3z).

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

Write the matrix of a linear operator given by the formula T(A)=AT with respect to this basis.

4. A linear operator has a matrix with respect to the standard basis . Find the matrices of this operator with respect to the bases

(a)                              (b)

5. Prove that the composition of two rotations by angles and in is the rotation by the angle .