Write the following sets as a span of the minimum number of vectors
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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Write the following sets as a span of the minimum number of vectors. If this is not a span and why?
![The image shows the mathematical expression:
\[ V = \left\{ \begin{bmatrix} a & b \\ c & a \end{bmatrix} \mid a + b + c = 0 \right\} \subseteq \mathbb{M}_{2 \times 2}. \]
This expression defines a set \( V \) of 2x2 matrices. Each matrix in the set has the form:
\[
\begin{bmatrix} a & b \\ c & a \end{bmatrix}
\]
where \( a, b, \) and \( c \) are real numbers that satisfy the condition \( a + b + c = 0 \). The symbol \(\subseteq\) indicates that \( V \) is a subset of \(\mathbb{M}_{2 \times 2}\), the set of all 2x2 matrices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc495729c-fc87-4b7b-a937-12ad0926c14e%2F7c1971a7-40bd-424e-9119-67ee6472c68f%2F8ogbxdk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows the mathematical expression:
\[ V = \left\{ \begin{bmatrix} a & b \\ c & a \end{bmatrix} \mid a + b + c = 0 \right\} \subseteq \mathbb{M}_{2 \times 2}. \]
This expression defines a set \( V \) of 2x2 matrices. Each matrix in the set has the form:
\[
\begin{bmatrix} a & b \\ c & a \end{bmatrix}
\]
where \( a, b, \) and \( c \) are real numbers that satisfy the condition \( a + b + c = 0 \). The symbol \(\subseteq\) indicates that \( V \) is a subset of \(\mathbb{M}_{2 \times 2}\), the set of all 2x2 matrices.
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