27. Let S be the set of all vectors both of y in R' such that x + y -z = 0 and 2x – 3y + 2z = 0. Show that S with the standard componentwise operations is a vector space. %3D -
27. Let S be the set of all vectors both of y in R' such that x + y -z = 0 and 2x – 3y + 2z = 0. Show that S with the standard componentwise operations is a vector space. %3D -
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 45EQ
Question
![**Problem 27.**
Let \( S \) be the set of all vectors
\[
\begin{bmatrix}
x \\
y \\
z
\end{bmatrix}
\]
in \( \mathbb{R}^3 \) such that \( x + y - z = 0 \) and \( 2x - 3y + 2z = 0 \). Show that \( S \) with the standard componentwise operations is a vector space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa00d0151-b5df-4ee3-a0d6-fdfba7d1c4f7%2F1a9142bf-ed6c-45ad-b829-a2f5796d3771%2Fl39y3x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 27.**
Let \( S \) be the set of all vectors
\[
\begin{bmatrix}
x \\
y \\
z
\end{bmatrix}
\]
in \( \mathbb{R}^3 \) such that \( x + y - z = 0 \) and \( 2x - 3y + 2z = 0 \). Show that \( S \) with the standard componentwise operations is a vector space.
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