2 points) Let H be the subspace of P2 spanned by 2x2 - 6x +3, x2 -2x 1 and -2r221 (a) A basis for H is Enter a polynomial or a list of polynomials separated by commas, in terms of lower-case x . For...
Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 8x−5x2+3, 2x-2x2+1 and 3x2-1. a) The dimensions of the subspace H is ___________? b) Is {8x-5x2+3, 2x-2x2+1, 3x2-1} a basis for P2? ________(be sure to explain and justify answer) c) A basis for the subspace H is {_________}? enter a polynomial or comma separated list of polynomials
Previous Problem Problem List Next Problem (1 point) Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 10x2 - 9x - 4, 12x2 - 10x 5 and 31x - 38x2 16. a. The dimension of the subspace H is 1 b. Is (10x2-9x-4,12x2- 10x - 5,31x -38x2+ 16) a basis for P2? choose Be sure you can explain and justify your answer. c. A basis for the...
(1 point) Let P, be the vector space of all polynomials of degree 2 or less, and let 7 be the subspace spanned by 43x - 32x' +26, 102° - 13x -- 7 and 20.x - 15c" +12 a. The dimension of the subspace His b. Is {43. - 32" +26, 10x - 13.-7,20z - 150 +12) a basis for P2? choose ✓ Be sure you can explain and justify your answer. c. Abasis for the subspace His { }....
(1 point) Let Ps be the vector space of all polynomials of degree at most 3, and consider the subspace 11 = {r(z) e Pal p(1) = 0} of P3 a A basis for the subspace H is { 22x+12x^2-x-1 Enter your answer as a comma separated list of polynomials. b. The dimension of His 3 (1 point) Find a basis for the space of symmetric 2 x 2-matrices If you need fewer basis elements than there are blanks provided,...
Let h(x) = 14), where f(x) = –2x – 3 and g(x) = x2 – x + 2. What is h' (x)? Select the correct answer below: 2x2 +6x–7 *4–2x3 +5x2–4x+4 -6x2–2x-1 x+-2x3 +5x2-4x+4 2x2+6x–7 x-x+2 O za
Write the polynomial f(x) as a product of irreducible polynomials in the given ring. Explain in each case how you know the factors are irreducible. 1) f(x) -x* + 2x2 +2x 2 in Z3[x]. 2) f(x)4 + 2x3 + 2x2 +x + 1 in Z3[x]. 3) f(x) 2x3-x2 + 3x + 2 in Q[x] 4) f(x) = 5x4-21x2 + 6x-12 in Q[x)
Let {p0, p1, p2} be a basis for a subspace V of ℙ3, where the pi are given below, and let the inner product for ℙ3 be given by evaluation at 0, 1, 2, 3, so <p,q> = p(0)q(0)+p(1)q(1)+p(2)q(2)+p(3)q(3). Use the Gram-Schmidt process to produce an orthogonal basis {q0, q1, q2} for V and enter the qi below. p0 = x−1 p1 = x2−2x+2 p2 = −3x2+2x q0 = q1 = q2 =
Q1 17 Points Let T: M2x2(R) P2(R), H (2a +b)x2 + (6 – c)x +(c – 3d). Let B = (16 0) (0 :), (1 o) 9)) = (6 7')(*: -) ) 6 :-)) B' = C = (x2,æ, 1) C'= (x + 2, x + 3, x2 – 2x – 6). You may assume that all of the above are bases for the corresponding vector spaces. Q1.1 2 Points Show that T is linear. Q1.2 9 Points Compute [T),...
Will rate once all is completed. 1) 2) 3) 4) (12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...
Let P2 be the vector space of polynomials of lower or equal degree at 2 with the scalar product: Let p1 (x) = 1 and p2 (x) = 2x - 1, two polynomials of P2. 1) Show that B = {p1, p2} forms an orthogonal set of P2. 2) Complete B to get a P2 base. 3) Let W = Vect {p1 (x), p2 (x)} be a vector subspace of P2, to determine W ⊥. Ensembles orthogonaux et bases orthogonales...