Find the orthogonal projection of12=onto the subspace W of R4 spanned by859projw (v) Use the inner product(§, 9) = for f(x)9(x) dxin the vector space P₂ of polynomials of degree at most 2 to find the orthogonal projection of f(x) = 2x² + 1 onto the subspace V spanned byg(x) =x and h(x) = 1. (Caution: x and 1 do not form an orthogonal basis of V.)projy(f) ==0.

Answered: Image /qna-images/answer/03256ee2-0748-4225-85c5-0bea00dd0e0f.jpg

Answered: Find the orthogonal projection of 12 =…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

See similar textbooks

Similar questions

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Find a basis for R2 that includes the vector (2,2).
{3} Find a in R² whose coordinate vector relative to the basis B is [*]B Let B: = x = 12 -5 = -6 [:] 5
solve parts a and b
TH Let B = {1, x, x², x³} be an ordered basis for P3. Find the coordinate vector of f(x)=-3x3+7x2+8x + 2 relative to B. fB=
2. The vector x = H [13] vector [2]B = [8] A 1 B 2 3 D0 in R2 relative to the orthogonal basis B What is the value of a + b? {0-[-]} has coordinate
Find the basis of subspace defined as S = {(a, b, c)|a - b +2c=0}.
I need help with this problem
Suppose y1 ( x), y2 ( x), y3 ( x) are three different functions of x. The vector space they span could have dimension 1, 2, or 3. Give an example of y1, y2, y3 to show each possibility.
Let X ∈ R3 be some xed vector with coordinates X1, X2, X3. Consider the action on vectors of the operator “cross-product by X”. In other words, it transforms vectors using the rule v → X × v. Since this is a linear operator, it is represented by some 3 × 3 matrix. Find this matrix in terms of X1, X2, X3. Is this matrix ever invertible?
[1 2] Let A Write the vector u = (4,3) as u = u, + un where u, and un 3 belong to the row space and nullspace of A, respectively.
Consider matrix A = Answer: 0 1 (₁2) G -1 2 and vectors x = (¹2₂) and y = (1). . Calculate matrix B = (A – AT)² and vector w = Bx. Then, evaluate the scalar product w · y. [Please enter your answer numerically. You will be marked correct as long as what you enter is within 0.5 of the correct answer.]

Recommended textbooks for you

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS