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).
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Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
#9 a,b, and c
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b5c85cb-60d8-4aa4-b6f6-3a8d554b379e%2F5f1e0fd5-ab5f-431a-b8ee-57bbba20e695%2Fb2pdql.jpeg&w=3840&q=75)
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