answer Yes/ No only in the following 5 questions; no work need be shown.

1. Let T : C2 - C2 be a linear operator and C2 = U OW where dim U = 1 = dim W. If for fixed complex number c, Tu = cu for u E U, then Twe W. 2. Let M(T) = a C b be a complex matrix. Then T is self-adjoint. 3. Let M(T) = a C d b where a, b, c, d are reals. Then its eigenvalues are real numbers. 4. If T = Re is the rotation operator acting on R2, and Tv = Av for some nonzero vector v E R2, then T*v = Xv. 5. There are no real non-symmetric 3 by 3 matrices with 3 linearly independent eigen- vectors