Determine whether the statement below is true or false. Justify the answer. The vectors are in R". If x is orthogonal to every vector in a subspace W, then x is in wt. Choose the correct answer below. O A. The statement is false. A vector x is in w- if and only if x is orthogonal to every vector in a set that spans W. O B. The statement is true. If x is orthogonal to every vector in W, then x is said to be orthogonal to W. The set of all vectors x that are orthogonal to W is denoted w O C. The statement is true. If x is orthogonal to every vector in a subspace W, then x = 0. The zero vector is in every subspace, so x must be in W+ O D. The statement is false. If x is orthogonal to every vector in a subspace W, then x is in W and so x cannot be in w+

Determine whether the statement below is true or false. Justify the answer. The vectors are in R". If x is orthogonal to every vector in a subspace W, then x is in wt. Choose the correct answer below. O A. The statement is false. A vector x is in w- if and only if x is orthogonal to every vector in a set that spans W. O B. The statement is true. If x is orthogonal to every vector in W, then x is said to be orthogonal to W. The set of all vectors x that are orthogonal to W is denoted w O C. The statement is true. If x is orthogonal to every vector in a subspace W, then x = 0. The zero vector is in every subspace, so x must be in W+ O D. The statement is false. If x is orthogonal to every vector in a subspace W, then x is in W and so x cannot be in w+

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 42CR: Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a...

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