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+
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine whether the statement below is true or false. Justify the answer. The
Transcribed Image Text: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.
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+.
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