Exercise 5. Let L Q5 Q5 e the linear operator defined by a, b, c, d, e) E (2a e, -a 2b, c 3d, -2c d, a-b 2e) Part 1 (1.1) Find the number k such that e1, L (e1), LR-1 (e1) are l.i., but L (e1) is linearly dependent to e1, L -1 (e) (1.2) Write a basis for the cyclic subspace of e 1, i.e. Ce1. (1.3) Write L3(e1) as a linear combination of e1, L(e1), L (e1) (1.4) rite its companion matriz, i.e write the matriz representing Cer with re spect to the basis e1, L(e1),..., LK-1(e1) Solution L[U]=L*U=V.