試題詳解

十、Let , be a linear transformation on for a rotation by an angle θ about a unit vector
u. Specifically, we let the matrix for with respect to the standard basis S for be

where is the coordinate vector of u with respect to S, c = cos(θ)
and s = sin(θ). Furthermore, let A be the rotation matrix about the z-axis of Cartesian
coordinate system by an angle θ, i.e.,

where be an ordered orthonormal basis for with
and let be the change
of-basis matrix for changing basis from B to S. Which of the following statements is/are
true?
(A), n₁n₂ +b₁b₂ + u₁u₂ = 0 and n₁n₃ + b₁b₃ +u₁u₃ =0.
(B) The coordinate vector of u with respect to basis B is .
(C)
(D)
(E) The matrix for with respect to basis B is A.