If the statement is true, write a complete step-by-step proof of the statement. If the statement is false, give a specific counterexample, and provide the justification that the counterexample proves the statement false. Let V₁, V2, V3, and w be vectors in R³. If w is orthogonal to each of the vectors V₁, V2, and V3, then w belongs to the set (Span {V1, V2, V3})+
If the statement is true, write a complete step-by-step proof of the statement. If the statement is false, give a specific counterexample, and provide the justification that the counterexample proves the statement false. Let V₁, V2, V3, and w be vectors in R³. If w is orthogonal to each of the vectors V₁, V2, and V3, then w belongs to the set (Span {V1, V2, V3})+
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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![**Instructions for Proof or Counterexample:**
If the statement is true, write a complete step-by-step proof of the statement. If the statement is false, give a specific counterexample, and provide the justification that the counterexample proves the statement false.
**Statement:**
Let **v₁, v₂, v₃**, and **w** be vectors in ℝ⁵. If **w** is orthogonal to each of the vectors **v₁, v₂,** and **v₃**, then **w** belongs to the set
\[
( \text{Span} \{ \mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3 \} )^\perp
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6e6d380-54a4-46c8-adc0-56f54d5d0909%2Fdb7378a8-16cc-4387-aee8-3863e6c3326b%2Fbsmc0r9_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions for Proof or Counterexample:**
If the statement is true, write a complete step-by-step proof of the statement. If the statement is false, give a specific counterexample, and provide the justification that the counterexample proves the statement false.
**Statement:**
Let **v₁, v₂, v₃**, and **w** be vectors in ℝ⁵. If **w** is orthogonal to each of the vectors **v₁, v₂,** and **v₃**, then **w** belongs to the set
\[
( \text{Span} \{ \mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3 \} )^\perp
\]
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