V = a C |a+b+c= 2, 3a - c = 1, a-b+c=3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Is this a subspace of R3? Please explain it.

Transcribed Image Text:**Vector Definition and System of Equations**
The image describes a set \( V \) of vectors, where each vector \(\begin{bmatrix} a \\ b \\ c \end{bmatrix}\) satisfies the following system of linear equations:
1. \( a + b + c = 2 \)
2. \( 3a - c = 1 \)
3. \( a - b + c = 3 \)
This notation is often used in linear algebra to define a subspace or solution set in \(\mathbb{R}^3\), the three-dimensional real coordinate space. The conditions ensure that any vector \(\begin{bmatrix} a \\ b \\ c \end{bmatrix}\) in the set \( V \) simultaneously satisfies all three equations.
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We know that any subspace of a vector space should contain the zero vector of the vector space.
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