Question

Let T є L(C3) be defined by T(r, y, z)-(y-2-2c, z-2-2y,1-2y-22). (a) Is span((1,1,1)) invariant under T? (b) Is U = { ( (c) Is U = {(x, y, z) : x + y + z = 0} invariant under T? (d) Is λ 2 an eigenvalue of T? Is T-21 injective? (e) Find all eigenvectors of T associated to the eigenvalue λ =-3. 4. r, y,r-y) : x, y E C} invariant under T?

Answer 1

Then T Cadd Ans- u - - 22 2

(3 2

exe 20-2 C 2b-2c Hence o is 7-inva o Ts T-21 is njective :2 is an eigen value of ip then Some mon zero

2. 2 2

Hence exis 6uch that zez。.ve d o γ· do the eigem value X3 hs - uch that 令

2. The Se of eigen veclsr u e