Determine whether the statement below is true or false. Justify the answer. The set Span {u, v} is always visualized as a plane through the origin. Choose the correct answer below. A. The statement is true. The set Span {u, v} is always visualized as a plane in R³ that contains u, v, and 0. B. The statement is false. It is often true, but Span {u, v} is not a plane when v is a multiple of u or when u is the zero vector. C. The statement is true. The set Span {u, v} is always visualized as a line in R³ that contains u, v, and 0. O D. The statement is false. Although the set Span {u, v} is always visualized as a plane, it is not always through the origin.
Determine whether the statement below is true or false. Justify the answer. The set Span {u, v} is always visualized as a plane through the origin. Choose the correct answer below. A. The statement is true. The set Span {u, v} is always visualized as a plane in R³ that contains u, v, and 0. B. The statement is false. It is often true, but Span {u, v} is not a plane when v is a multiple of u or when u is the zero vector. C. The statement is true. The set Span {u, v} is always visualized as a line in R³ that contains u, v, and 0. O D. The statement is false. Although the set Span {u, v} is always visualized as a plane, it is not always through the origin.
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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Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer.
The set Span {u, v} is always visualized as a plane through the origin.
Choose the correct answer below.
A. The statement is true. The set Span {u, v} is always visualized as a plane in R³ that contains u, v, and 0.
B. The statement is false. It is often true, but Span {u, v} is not a plane when v is a multiple of u or when u is the zero vector.
OC. The statement is true. The set Span {u, v} is always visualized as a line in R³ that contains u, v, and 0.
3
D. The statement is false. Although the set Span {u, v} is always visualized as a plane, it is not always through the origin.
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