Homework Answers
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 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...
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.
3. Let S = (x2 + t.t-1.1 +1} be a subset of V =P (a) If...
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
(1 point) Let S-(r, u, d, x) be a set of vectors. If x = 4r...
(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+
(a). Determine whether the set is linearly dependent or independent. Further, if it is linearly dependent,...
(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...
please help with this linear algebra question Question 10 [10 points] Let V be a vector...
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 >
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearl...
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
2. (a) Let B = {f1, f2, f3} be a subset of P2 where fi(x) =...
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)...
Determine which of the sets of vectors is linearly independent. Determine whether the vectors x2 -1,...
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
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
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.
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
(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+
(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...
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 >
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
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)...
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
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
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