Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
V = a C |a+b+c= 2, 3a - c = 1, a-b+c=3

V = a C |a+b+c= 2, 3a - c = 1, a-b+c=3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Is this a subspace of R3? Please explain it.
**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.
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.
Expert Solution
Step 1

We know that any subspace of a vector space should contain the zero vector of the vector space.

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS