For the following questions, you just need to circle one of answers. .s points/each, totally 8...
2. For the following questions, you just need to circle one of answers. (1.5 points/each, totally 8 points) Let , be the set of all polynomials with exact degree 2. Is this a subspace of a,17(Yes b. Given 2 by 2 matrix A. S-(BeR 1AB BA) is a subspace of vector space R7 a. No) (Yes No) 1 AB-0), is S asubspace of 2 by 2 c. Given 2 by 2 matrix A. Let s- (Be R matrix vector space?...
2. For the following questions, you just need to circle one of answers. (1.5 points/each, totally 8 points) Let , be the set of all polynomials with exact degree 2. Is this a subspace of a,17(Yes b. Given 2 by 2 matrix A. S-(BeR 1AB BA) is a subspace of vector space R7 a. No) (Yes No) 1 AB-0), is S asubspace of 2 by 2 c. Given 2 by 2 matrix A. Let s- (Be R matrix vector space?...
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...
How do I do these linear algebra questions?
The question is:
Consider the Vector Space V and its subset W given below.
Determine whether W forms a subspace of V. If your answer is
negative then you must provide which subspace requirement is
violated.
(b). V is P5, the vector space of all polynomials in x of degree s5 and W is the set of all polynomials divisible by x – 3. (c). V is P5, the vector space of...
HW08 vector spaces subspaces: Problem 8 Next Problem Previous Problem Problem List (1 point) Determine whether the given set S is a subspace of the vector space V. f those functions satisfying f(a) = f(b). A. V is the vector space of all real-valued functions defined on the interval la, b, and S is the subset of V consisting B. V C1 (R), and S is the subset of V consisting of those functions satisfying f'(0) > 0. , _D...
(1 point) Determine whether the given set S is a subspace of the vector space V. A. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed mxn matrix. B. V is the vector space of all real-valued functions defined on the interval (-oo, oo), and S is the subset of V consisting of those functions satisfying f(0) 0 C. V Mn (R), and S is the...
Given the vector space R[2]deg<s of polynomials with real coefficients of degree at most 5, and Ui = {p(z) : p(z) a? + bz5, for abe R}, find a subspace U2 such that R deg< 5 = Ui φ Ủy Is this U2 unique? (g) If V be a finite dimensional vector space, dim V = n and B = 〈ui,u2, . . . , un) is a basis of V, then show that:
Name: Math 23 6. (14 points) Determine whether the following subsets are subspaces of the given veeto r space. Either prove that the set is a subspace or prove that it is not (a) The subset T C Ps of polynomials of degree less than or equal to 3 that are of the form p(x)-1+iz+o2+caz3, where c,02, c3 are scalars in R. (b) The set s-a a,bERM22, that is, the subset of all 2 x 2 matrices A where a11-a22...
7. Let V = Pa(R), the vector space of polynomials over R of degree less than 2, with inner product Define φ E p by φ(g)-g(-1) a) By direct calculation, find f e V such that (S)-dg). You are given that A 1, V3-2v) is an orthonormal basis for V (you do not need to check this). b) Find the same f as in part a, using the formula for A(6) from class.
7. Let V = Pa(R), the vector...
Please explain in DETAIL on how to obtain the answers.
THE ANSWERS ARE PROVIDED.
PLEASE SHOW WORK.
Solve the problem 5) Determine which of the following statements is false A: The dimension of the vector space P7 of polynomials is 8 B: Any line in R3 is a one-dimensional subspace of R3 C: If a vector space V has a basis B.3then any set in V containing 4 vectors must be linearly dependent. A) A Objective: (4.5) Know Concepts: The...