Homework Answers
the following vectors are
linearly independent in their respective vector space and have same
size as the dimension of their vector space. So they form a basis
for the vector space and hence spanning set of over the vector
spaces.
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1. For each of the following vector spaces, give two differ- ent spanning sets: (b) M22...
Are the following sets vector spaces? Give reasons. 2. a) pe P4 p(1) 0 and p(-1)...
Are the following sets vector spaces? Give reasons. 2. a) pe P4 p(1) 0 and p(-1) 0 }; b) (pe P3 ap'(x) c) pe P9 | p has degree 4 or more}. 2p(x) for all eR};
Are the following sets vector spaces? Give reasons. 2. a) pe P4 p(1) 0 and p(-1) 0 }; b) (pe P3 ap'(x) c) pe P9 | p has degree 4 or more}. 2p(x) for all eR};
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of R).
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a + 3b) (which is a subspace of R).
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all lower triangular 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, c, 2a + 3b – 3c) (which is a subspace of R4).
6. For the following vector spaces V, determine if the subset H is a subspace. If...
6. For the following vector spaces V, determine if the subset H is a subspace. If not, give one reason why H fails to be a subspace. (a) (5 points) V is the set of functions f from R + R, and H is the set of polynomials of integer coefficients. (b) (5 points) V = P, is the vector space of polynomials of degree at most 2, and H is the subset of all polynomials in P2 of the...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of Re"). 2. (12 pts) Given the matrix in a R R-E form: -21 1 [1 0 0 0 3 0 1 1 0 - 2 0 0 0 1 0...
9. Find the dimension of each of the following vector spaces (a) The vector space of...
9. Find the dimension of each of the following vector spaces (a) The vector space of all diagonal n xn matrices. (b) The vector space of all symmetric n x n matrices. (c) The vector space of all upper triangular n x n matrices
9. Find the dimension of each of the following vector spaces (a) The vector space of all diagonal n xn matrices. (b) The vector space of all symmetric n x n matrices. (c) The vector space...
2) Determine if each of the sets below is a vector space, give a basis if...
2) Determine if each of the sets below is a vector space, give a basis if it is a vector space or an explanation if it is not a vector space. Зр 2q -P p +9) p.q ER {[1]: a+c=0} ; T,S, ER 2t
4. (20 points) Determine whether the following sets are linear independent. Prove your statem ent. in...
4. (20 points) Determine whether the following sets are linear independent. Prove your statem ent. in the vector space of 2 × 2 matrices. b. (sinx, cos.x, 1 in the vector space CTo, 1].
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that...
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that the following set forms a basis for W: S = -5 (B.2) Obtain the coordinate vector for A = 3 relative to S. That is, find (A)s. -8 Show work!
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that the following set forms a basis for W: S = -5 (B.2) Obtain the coordinate vector for A...
Are the following sets vector spaces? Give reasons. 2. a) pe P4 p(1) 0 and p(-1) 0 }; b) (pe P3 ap'(x) c) pe P9 | p has degree 4 or more}. 2p(x) for all eR};
Are the following sets vector spaces? Give reasons. 2. a) pe P4 p(1) 0 and p(-1) 0 }; b) (pe P3 ap'(x) c) pe P9 | p has degree 4 or more}. 2p(x) for all eR};
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of R).
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a + 3b) (which is a subspace of R).
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all lower triangular 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, c, 2a + 3b – 3c) (which is a subspace of R4).
6. For the following vector spaces V, determine if the subset H is a subspace. If not, give one reason why H fails to be a subspace. (a) (5 points) V is the set of functions f from R + R, and H is the set of polynomials of integer coefficients. (b) (5 points) V = P, is the vector space of polynomials of degree at most 2, and H is the subset of all polynomials in P2 of the...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of Re"). 2. (12 pts) Given the matrix in a R R-E form: -21 1 [1 0 0 0 3 0 1 1 0 - 2 0 0 0 1 0...
9. Find the dimension of each of the following vector spaces (a) The vector space of all diagonal n xn matrices. (b) The vector space of all symmetric n x n matrices. (c) The vector space of all upper triangular n x n matrices
9. Find the dimension of each of the following vector spaces (a) The vector space of all diagonal n xn matrices. (b) The vector space of all symmetric n x n matrices. (c) The vector space...
2) Determine if each of the sets below is a vector space, give a basis if it is a vector space or an explanation if it is not a vector space. Зр 2q -P p +9) p.q ER {[1]: a+c=0} ; T,S, ER 2t
4. (20 points) Determine whether the following sets are linear independent. Prove your statem ent. in the vector space of 2 × 2 matrices. b. (sinx, cos.x, 1 in the vector space CTo, 1].
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that the following set forms a basis for W: S = -5 (B.2) Obtain the coordinate vector for A = 3 relative to S. That is, find (A)s. -8 Show work!
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that the following set forms a basis for W: S = -5 (B.2) Obtain the coordinate vector for A...
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