5) Given a subset S - lyx+z- -2(. Determine whether or not S is a subspace
Determine whether the subset S is a subspace of R" or not. If it is a subspace, explain why it is, either by checking that the three defining properties of a subspace are satisfied or by using a result from class (for insta that the span of vectors subspace which is not satisfied (e.g. specific vectors u and v are in S but iu ö is not in S), Studying examples 3.38, 3.39 and 3.40 in the textbook could be...
(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...
Determine whether the given set S is a subspace of the vector space V.A. V=C2(ℝ) (twice continuously differentiable functions), and S is the subset of VV consisting of those functions satisfying the differential equation y″=0. B. V=ℙ5, and SS is the subset of ℙ5 consisting of those polynomials satisfying p(1)>p(0)C. V=ℙ4, and SS is the subset of ℙ4 consisting of all polynomials of the form p(x)=ax3+bx.D. V=Mn×n(ℝ), and SS is the subset of all symmetric matrices.E. V=ℝ2, and S consists of...
Determine whether the given S is a linearly independent subset of the given vector space, V 1. 48- 4118 Determine whether the given S is a linearly independent subset of the given vector space, V 1. 48- 4118
Determine whether the given S is a linearly independent subset of the given vector space, V 1. 48- 4118
5. (6 points each) Determine whether or not Wis a subspace of R", for each of the subsets giv below: (For each subset, provide evidence to support your answer.) a. W = |b : a = c2 b. W =31b: 2a - b = (Icl
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...
2. In each of the following find out if the subset S is a subspace of the vector space V. (a) V = R3, S = {x = (x1,T2, xs) : 2x1-3x2 +23 = 6). 一 山 (c) V = R2, S = {x = (xi, X2) : X1X2 > 0}
QUESTION 2. (a) Decide whether each of the following subsets of R’ is a subspace. Either provide a proof showing the set is a subspace of R3, or provide a counterexample showing it is not a subspace: [9 marks] (i) S= {(x, y, z) ER3 : 4.0 + 9y + 8z = 0} (ii) S = {(x, y, z) E R3 : xy = 0} (b) Determine for which values of b ER, the set S = {(x, y, z)...
Determine whether each of the following is a subspace of the relevant R". (a) V1 = {(x, y, z) | x, y ER, Z E Z} (b) V2 = {(2,4,4) + s(1, 2, 2) + t(4,5,7) | ste R} (c) V3 = {(a, b, c, d) | a, b, c, d e R, ab = 0}