Please solve and show all work using Linear Algebra. 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.O A. The statement is false. Although the set Span (u, v) is always visualized as a plane, it is not always through the origin.O 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 zerovector.OC. 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 true. The set Span (u, v) is always visualized as a plane in R³ that contains u, v, and 0.

Given the is always visualized as a plane through the origin.The above statement is false. If v is…

Answered: Determine whether the statement below…

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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Please solve and show all work using Linear Algebra.

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.
O A. The statement is false. Although the set Span (u, v) is always visualized as a plane, it is not always through the origin.
O 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.
O D. The statement is true. The set Span (u, v) is always visualized as a plane in R³ that contains u, v, and 0.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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