### Linear Algebra Concept CheckThe set $ S = \{v1, v2, \ldots, vn\} $ is a spanning set for the vector space $ V $. This statement implies that any vector $ u $ in $ V $ can be written as a linear combination of the vectors in $ S $.#### Question:Is it true that any vector $ u $ in $ V $ can be written in one and only one way as a linear combination of the vectors in $ S $?##### Select one:- ○ True- ○ False

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The set S={v1, v2, ..., vn} is a spanning set for the vector space V, then any vector u in V can be written in one and only one way as a linear combination of vector of S. Select one: O True O False

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

### Linear Algebra Concept Check

The set $ S = \{v1, v2, \ldots, vn\} $ is a spanning set for the vector space $ V $. This statement implies that any vector $ u $ in $ V $ can be written as a linear combination of the vectors in $ S $.

#### Question:
Is it true that any vector $ u $ in $ V $ can be written in one and only one way as a linear combination of the vectors in $ S $?

##### Select one:
- ○ True
- ○ False

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