7. Let V and W be two vector space and L V -W be a linear transformation ker L is a subspace of V. 8. Determine whether the following are linear transformation in P, the set of poly (a) L(p(x)) a2...

#9 a,b, and c

Extracted text: 7. Let V and W be two vector space and L V -W be a linear transformation ker L is a subspace of V. 8. Determine whether the following are linear transformation in P, the set of poly (a) L(p(x)) a2 p(x) for p E P. (b) L(p(x)) = x2?p(x)+ p(x) for pe P. 9. (a) Show that L(f(a)) = f (x)f(0) is a linear operator in C[-1,1]. (b) Find ker L above. (c) Find the range of L above. 10. Let S {(x1, x2, x3 , X4)| x1+x2 = x3 + 4} be a subspace of R4. Find S- 11. Given v (1,-1,1,1) and w (4,2,2,1) (a) Determine the angle between v and w. Find the orthogonal complement of V = span {v, w}. 12. Let A be an m x n matrix. and AT).