469360.2546800.qx3zqy7Jump to level 1Let {u₁(x) = -6, u₂(x) = -12x, uz (x) = 12x²} be a basis for a subspace of P₂. Use the Gram-=[ f(x)g(x) dx onSchmidt process to find an orthogonal basis under the integration inner product (f.g)C[0, 1].Orthogonal basis: {v₁(x) = −6, v₂ (x) = − 12x + a, v³ (x) = 12x² +bx+c}a = Ex: 1.23b= Ex: 1.23c = Ex: 1.2325

Answered: Image /qna-images/answer/ca3d0802-da0c-4145-964d-b8d48e9b8e5e.jpg

Let {u₁(x) = −6, u₂(x) = − 12x, uz (x) = 12x²} be a basis for a subspace of P₂. Use the Gram- Schmidt process to find an orthogonal basis under the integration inner product (ƒ, g) [²ƒ(z)g(x) da on C[0, 1]. Orthogonal basis: {v₁(x) = −6, v₂ (x) = − 12x + a, v3 (x) = 12x² +bx+c} a = Ex: 1.23 b = Ex: 1.23 c = Ex: 1.23 S

Let {u₁(x) = −6, u₂(x) = − 12x, uz (x) = 12x²} be a basis for a subspace of P₂. Use the Gram- Schmidt process to find an orthogonal basis under the integration inner product (ƒ, g) [²ƒ(z)g(x) da on C[0, 1]. Orthogonal basis: {v₁(x) = −6, v₂ (x) = − 12x + a, v3 (x) = 12x² +bx+c} a = Ex: 1.23 b = Ex: 1.23 c = Ex: 1.23 S

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

Related questions

Q: Find the matrix A' for T relative to the basis B'. A' = T: R³ → R³, T(x, y, z) = (x, y, z), B' =…

Q: Find the matrix A' for T relative to the basis B'. A' = T: R² → R², T(x, y) = (x − y, y - 2x), B' =…

Q: Find the coordinate matrix of x in R^ relative to the basis B'. B' = {(5, 0), (0, 2)}, x = (10, 8)…

A: If A is a basis, then x∈Rn can be written as linear combination of the elements of A. When a scalar…

Q: Let S = {i, j} is a basis of R² and let W = {(x, y), x + y = 0} a- Show that W is subspace of R², b-…

Q: Q2) (a) Use the definition = ]f(t)g(t)dt in T0,1] to find the components of f(t)=2+t in the…

Q: Consider P2 (R) together with inner product: Find an orthogonal basis for P2 (R). (p(z),9(2) = Г'р…

Q: Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x, y, z) = (y + z, x + z, x − y),…

Q: The vector x is in a subspace H with a basis B = {b₁,b₂). Find the B-coordinate vector of x. 2 b₁ =…

A: We are given that b1 = (2, -3)t b2 = (-1, 5)t Now, x is in H with the…

Q: Consider P(t) with inner product = ∫ f(t)g(t)dt and the subspace W=P3(t). Find the orthonormal…

Q: Let V R2[x] be the real vector space of polynomials of degree at most 2. Let {fo, f1, f2} with fo(x)…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Let c1 (t) = ei + 7 sin(t)j + t*k and c2 (t) = e-Sti + 5 cos(t)j – 7t*k. (Enter your solution as a…

A: Given: Let c1(t)=e5ti+7sintj+t4k and c2(t)=e-5ti+5cos(t)j-7t4k. To Find: ddt[c1(t)+c2(t)]

Q: Let {u₁(x) = 12, u₂(x) = − 18x, uz (x) = 8x²} be a basis for a subspace of P2. Use the Gram-Schmidt…

Q: Let V be the vector space of functions spanned by Nπ B = {b₁ = 5 sin x + 7 cos x, b₂ = 3 sin x + 9…

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(-8, 9), (3, –2)}, x = (-37,…

Q: Find a basis {p(x), g(x)} for the vector space {f(x) = P₂[x] | f'(3) = f(1)} where P₂ [x] is the…

A: Here we have to find the p(x) and q(x) that are basis of given vector space.

Q: Let V = P² be the vector space of polynomials of degree at most 2, and let B be the basis {f1, f2,…

Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (x – y, y – 4x), B' = {(1,…

A: The given transformation is Tx,y=x-y,y-4x and the basis B'1,-2,0,3.

Q: Find the matrix A' for T relative to the basis B'. A' = T: R² → R², T(x, y) = (x − 3y, y − x), B' =…

A: Please refer to the solution in next step.

Q: Let p₁ (t) = 7+t², P₂ (t)=t-2t², P3(t) = 2+t-4t². Complete parts (a) and (b) below. a. Use…

A: The polynomials p1t, p2t and p3t belongs to the vector space P2 because P2 contains all the…

Q: Find a basis {p(x), q(x)} for the vector space {ƒ(x) = P₂(x) | ƒ'(8) = ƒ(1)} where P₂(x) is the…

A: For any vector f(x) ∈ P2(x) , there exist scalars a, b, and c such that f(x) = a + bx + cx2…

Q: 2. Consider the subspace im(A) of Rº, where 1 1 A = | 1 1 3 Find a basis of ker(A"), and draw a…

A: Given matrix A=111213 AT=111123

Q: The vector x is in a subspace H with a basis ß = {b₁,b₂}. Find the ß-coordinate vector of x. b₁ =…

A: The given basis is b1,b2=1-2, -53. To Find: beta coordinate vector of x=19-17 w.r.t the above basis.

Q: 3. Let S be the subspace of R' given by S = {(x1, x2, T3, T4) : x1 – 2x2 + 4.x3 – 3x4 = 0} %3D - a.…

Q: Find the coordinate matrix of x in Rº relative to the basis B'. B' = {(3, 0), (0, 8)}, x = (24, 16)…

A: Given the basis B'=3,0,0,8 and x=24,16 Let x1, x2 is coordinate vector that is xB'=x1x2 Then it…

Q: Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x − y, 5y − x), B' = {(1,…

Q: Find the coordinate vector [x]R of x relative to the given basis B= {b1, b2, b3}. 1 4 1 - 6 b, 0 ,…

Q: Find the coordinate vector [x]B of x relative to the given basis B= {b1, b2} b1 b2 - 3 %3D X = - 10…

Q: Find the coordinate vector [x]R of x relative to the given basis B= {b1.b2}. 3 b1 b2 - 2 X= 4 [x]g =

Q: Find the B-coordinate vector of x E H where B = {b₁,b₂} is a basis of subspace H. b₁ = H b₂ = [6] 3…

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

A: The given vector space is with basis B'=4,3,3, -11,0,11, 0,9,2. Consider the vector x=26,3,-19∈R3.…

Question

469360.2546800.qx3zqy7
Jump to level 1
Let {u₁(x) = -6, u₂(x) = -12x, uz (x) = 12x²} be a basis for a subspace of P₂. Use the Gram-
=
[ f(x)g(x) dx on
Schmidt process to find an orthogonal basis under the integration inner product (f.g)
C[0, 1].
Orthogonal basis: {v₁(x) = −6, v₂ (x) = − 12x + a, v³ (x) = 12x² +bx+c}
a = Ex: 1.23
b= Ex: 1.23
c = Ex: 1.23
2
5

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Finding a value

VIEW

Step 3: Finding b and c

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

CHALLENGE
ACTIVITY
7.5.2: Orthogonal projections.
469360.2546800.qx3zqy7
Jump to level 1
Find the orthogonal projection ŷ of y=
W = Span u₁=
ŷ =
Ex: 1.23
, U₂ =
-6
-5 onto the subspace
5
-3

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

3) Find a basis for the subspace of R' that consists of the intersection of the planes X 3Y = 5Z and X = 3Z
Let {u1 (x) = 12, u2 (x) = 12x, uz (x) = 8x2 } be a basis for a subspace of P2. Use the Gram-Schmidt process to find an orthogonal basis under the integration inner product (f, g) f(x)g(x) dæ on C[0, 1]. Orthogonal basis: {v1(x) = 12, v2 (x) 12x + a, v3 (x) = 8x² + bx +c} = а —D Еx: 1.23 b = Ex: 1.23 с — Еx: 1.23
Let {u₁(x) = 12, u₂(x) = 18x, uz (x) = −8x²} be a basis for a subspace of P2. Use the Gram-Schmidt process to find an orthogonal basis under the integration inner product (S. 9) = f(2)g(2) dæ on C[0, 1]. Orthogonal basis: {v₁(x) = 12, v₂ (x) = 18x + a, v3 (x) = a = Ex: 1.23 b = Ex: 1.23 c = Ex: 1.23 −8x² + bx+c}
Find the matrix A' for T relative to the basis B'. T: R² A' = X A' = 3 11/3 R², T(x, y) = (x - y, y - 2x), B' = {(1, -2), (0, 3)} -3 48 -16 -4 Find the matrix A' for T relative to the basis B'. ↓ 1 T: R² → R², T(x, y) = (-7x + y, 7x - y), B' = {(1, −1), (-1,5)} -72 24
The vector x is in a subspace H with a basis ß = {b₁,b2}. Find the ß-coordinate vector of x. b₁ = [+] °4 °H [1] O = X =
The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate vector of x. 1 -1. b₁ = 5 - 8 MG-18 [X] B b₂ - 1 |-*-[ X: 5 - 1
Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x + y, 5y), B' = {(-4, 1), (1, -1)} A' =
Find the matrix A' for T relative to the basis B'. T: R² A' = R², T(x, y) = (x + y, 3y), B' = {(-4, 1), (1, -1)}