Let W={a0+a1x+a2x2|a1,a1,a2∈R,a0+a1=0} be a subset of P2, the collection of all polynomials of degree ≤2. Let p=a0+a1x+a2x2∈W, q=b0+b1x+b2x2∈W and scalar k. Which of the following shows that W is a subspace of P2? A. 1−x+x2∈W, (a0+b0)+(a1+b1)=0 and ka0+ka1=0 B. (a0+b0)+(a1+b1)=0 and ka0+ka1=0 C. 1+x2∈W, (a0+b0)+(a1+b1)=0 and ka0+ka1=0 D. 1−x+7x2∈W, a0+a1=0, b0+b1=0 and ka0+ka1=0 E. 2−2x∈W, (a0+b0)+(a1+b1)=0 and ka0=0,ka1=0

Let W={a0+a1x+a2x2|a1,a1,a2∈R,a0+a1=0} be a subset of P2, the collection of all polynomials of degree ≤2. Let p=a0+a1x+a2x2∈W, q=b0+b1x+b2x2∈W and scalar k. Which of the following shows that W is a subspace of P2? A. 1−x+x2∈W, (a0+b0)+(a1+b1)=0 and ka0+ka1=0 B. (a0+b0)+(a1+b1)=0 and ka0+ka1=0 C. 1+x2∈W, (a0+b0)+(a1+b1)=0 and ka0+ka1=0 D. 1−x+7x2∈W, a0+a1=0, b0+b1=0 and ka0+ka1=0 E. 2−2x∈W, (a0+b0)+(a1+b1)=0 and ka0=0,ka1=0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 14x² − 17x + 10, 17x – 19x² – 11 and 9x² - 10x + 6. a. The dimension of the subspace H is b. Is {14x² - 17x + 10, 17x - 19x² – 11,9x² – 10x +6} a basis for P₂? choose c. A basis for the subspace H is { (where you can enter xx in place of x²) Be sure you can explain and justify your answer. }. Enter a polynomial or a comma separated list of polynomials
Evaluate the surface integrals F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy + yzj + zxk, S is the part of the paraboloid z = 2x² - y² that lies above the square 0 ≤ x ≤ 1,0 ≤ y ≤ 1, and has upward orientation
Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by - 3x + 2, 12x – 7x2 – 2 and 3x2 – 3x + 1. 5x2 a. The dimension of the subspace H is b. Is {5æ? . - 3x + 2, 12x – 7x? – 2, 3x? – 3x + 1} a basis for P2? c. A basis for the subspace H is {
Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 3x² - 2x - 1, 12x²-6x - 5 and 22x 45x2+ 19. - a. The dimension of the subspace H is ☐. b. Is {3x² - 2x 1, 12x²-6x-5, 22x45x² + 19} a basis for P2? choose - Be sure you can explain and justify your answer. c. A basis for the subspace H is { ☐ }. Enter a polynomial or a comma separated list of polynomials.
H. W let s ; X70, YER a subset of R². IS of 1R² -Jubol be Subspace
One of the following subsets of R is not subspace. Select one: a. lifER S={ b. S= X2 S= X2.
Which of the following constraints results in the set of all polynomials of the form ao + a₁ + a₂x² forms a subspace of P₂ (R)? Select all the correct options. ao = a₁ = a2 = 0 a₁ = 0 ao ≥ 0 2a1a2
Which of the following is/are subspaces of R³? V₁ = R² 0 a 1 {[A] {B} V₂ = V3 = Span O V₁ and V₂ O V₁ and V3 O V₁ only O V3 only O V/₂ only } : a is a real number.
Let fi = 1+2x + 3x², f2 = 2 + 3x + 4x². B = (f1, f2) is a basis for the subspace V = {ao +a1x+azx²[ao – 2a1 +a2 = 0} of R2[r]. Let g = 1+5x + 9x². If [g]g = (,) then s = a) -7 b) -5 c) 5 d) 7 e) g is not in V.
Which of the following is a subspace of the vector space P2 of all polynomials of degree at most 2? Select one or more: O a. The set of all polynomials of degree at most 1 O b. {ao +a1r + a2x2 E P2 : ao = 4} Oc. {ao +a1r + a2x E P2: a1 + a2 = 3} %3D d. {1+x+ x}
Define the subset V, of R3 to be the set of all vectors y in R satisfying x +y+z = r, where r is a real number. Determine all values of r for which V, is a subspace of R³. Justify your answer.