If the statement is true, prove it. Otherwise give a counter example.

a)If V=C3 and W1={(z1,z2,z2)C3:z1,z2C}, W2={(0,z,0)C3:zC}, then V=W1W2.

b)If Vis a vector space and W1, W2 are subspaces of V, then W1W2 is also a subspace of V.

c)If T:VV is a linear operator, then Ker(T) and Range(T) are invariant under T.

d)Let T:VV be a linear operator. If Ker(T)Range(T) ={0}, then V=Ker(T)Range(T).

e)If T1,T2:VV are linear operators such that T1T2=T2T1, and 2 is an eigenvalue of T2, then Ker(T22I) is invariant under T1.