Let S={2,3+x,1−x2}, p(x)=2−x−x2 and V=P2
(a) If possible, express p(x)as a linear combination of vectors in S.
(b) By justifying your answer, determine whether the set S is linearly independent or linearly dependent.
(c) By justifying your answer, determine whether the set S is a basis for P2
Please solve it in very detail, and make sure it is correct.
Let S={2,3+x,1−x2}, p(x)=2−x−x2 and V=P2 (a) If possible, express p(x)as a linear combination of vectors in...
Let S = {2,3 + x, 1 – x2}, p(x) = 2 - x - x2 and V = P2. (a) If possible, express p(x) as a linear combination of vectors in S. (b) By justifying your answer, determine whether the set S is linearly independent or linearly dependent. (c) By justifying your answer, determine whether the set S is a basis for P2.
Let T:P1→P2 be a linear transformation defined by T(a+bx)=3a−2bx+(a+b)x2. (a) Find range(T) and give a basis for range(T). (b) Find ker(T) and give a basis for ker(T) (c) By justifying your answer determine whether T is onto. (d) By justifying your answer determine whether T is one-to-one. (e) Find [T(7+x)]B, where B={−1,−2x,4x2} Please solve it in very detail, and make sure it is correct.
s=3 Let sor,+r,+r, = . Determine whether the set 2-X.SX-X?.6-(s+1)x+x' in P, is early independent or linearly dependent. If the set is linearly dependent then write one of the tors as a linear combination of the other two vectors in the set.
(1 point) Let S-(r, u, d, x) be a set of vectors. If x = 4r + u + d, determine whether or not s is linearly independent. Select an Answer '1. Determine whether or not the four vectors listed above are linearly independent or linearly dependent. If S is dependent, enter a non-trivial linear relation below. Otherwise, enter O's for the coefficients. d+
Determine which of the sets of vectors is linearly independent. Determine whether the vectors x2 -1, x2 + x -2, and x2 + 3x + 2 are linearly independent or linearly dependent in P2. A) Linearly Dependent B) Linearly Independent
Q3. Determine whether the set of vectors in P2 is linearly dependent or linearly independent. S= {2 - x, 4x – x², 6-7x + x>). Q4. Show that the following set is a basis of R. --00:07)}
please help with this linear algebra question Question 10 [10 points] Let V be a vector space and suppose that {u, v, w is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. a) {-v-3w, 2u+w, -u-2v} is linearly independent b) {-3v-3w, -u-w, -3u+3v} < Select an answer >
(a). Determine whether the set is linearly dependent or independent. Further, if it is linearly dependent, express one of the polynomials as a linear combination of others. (b). Determine whether the set can be considered as a basis of the vector space P2, which is the set of all polynomials of degree not more than 2 under addition and scalar multiplication. (1). B = {1 – 2,1 – 22, x – x2} (Hint: Similar to the matrix case in last...
3. Let S = (x2 + t.t-1.1 +1} be a subset of V =P (a) If possible, express 71284 +9 as a linear combination of the polynomials in S. (b) Determine whether or not S is a basis for V = P. 4. Find all values of a for which {[ 22 0 1],[0 a 2] [101]} is a basis or Rs
2. (a) Let B = {f1, f2, f3} be a subset of P2 where fi(x) = x² – 3, f2(x) = x2 – 2x and f3(x) = x. Show that B is a basis of P2. (b) Determine whether or not the following sets are subspaces of F. (i) X = {f € F | f(x) = a(x + cos x), a € R}. (ii) Y = {f EF | f(x) = ax + sin x, a € R}. (c)...