Answered: 3.8.) Using the Gram- Schmidt method,… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 71E

See similar textbooks

Related questions

Question

3.8

3.8.)
Using
the Gram-Schmidt method, turn the basis
B=Cb₁,b₂) of a two-dimensional subspace VCIR³ into an
ONB (= (₁₂₁ (₂) of U, where
b₂
b₁: =
1

Expert Solution

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Find a basis for the subspace given by the plane −3x + 2 y + 5z = 0.
Find a basis for the given subspace of R', and state its dimension for the plane 4x-2y+5 z = 0. V1 = 1 V2 = 1 0.8 0.4 1 V1 = V2 = 0.8 0.4 V1 = 1 V2 = -0.8 0.4 V1 = 1 , V2 = -0.8 0.4 V1 = V2 = -0.8 0.4
2. Find a basis and the dimension of the subspace W = {(0,a+b,a-b); a,be R} of R'.
A. 2. Find the Basis of the following subspaces of R³: (a) the Plane 5x - 4y + 3z = 0 (b) the line r = 6t , y = 7t, z = 8t, te R.
3) Find a basis for the subspace of R' that consists of the intersection of the planes X 3Y = 5Z and X = 3Z
3.8 Using the Gram-Schmidt method, turn the basis B = (b1, b2) of a two- dimensional subspace U C R into an ONB C = (c1, c2) of U, where bị := b2 :=
Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W. y = 1 Uz = u, = - 1 1. -2 (Type an integer or simplified fraction for each matrix element.)
5) Find a basis and the dimension of the subspace of R³ : W = {(x, y, z) : x - 2y + 3z = 0}
Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W. 3 - 1 2 u, = 2 uz = 1 y = uz = - 1 1 - 1 1 ... y = (Type an integer or simplified fraction for each matrix element.)
It's a Linear Algebra Problem: Execute the Gram-Schmidt process on the following two vectors to find an orthonormal basis set: v1=(2,2),v2=(4,0). After normalization, we have two new vectors u1=(x1,y1) and u2=(x2,y2). What is the value of x2? (rounded to nearest 3 decimal places)
Find the closest point to y in the subspace W spanned by u₁ and 2. 1 y = 16 [9.4 2 0 , U₁ = 0 7 U2 = 2 1 2

Recommended textbooks for you

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS