ermine whether the following matričèš are lihea 31 m3 m4 = , m2
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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I am confused about how to approach. I know if there is a free variable that it is linearly dependent but how do I approach that from matrices?
![Determine whether the following matrices are linearly independent or linearly dependent in \( M_{22} \).
\[ m_1 = \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}, \quad m_2 = \begin{bmatrix} 2 & 3 \\ 4 & 0 \end{bmatrix}, \quad m_3 = \begin{bmatrix} 0 & 1 \\ -1 & 5 \end{bmatrix}, \quad m_4 = \begin{bmatrix} 2 & 0 \\ 1 & -3 \end{bmatrix} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fe79bd2-2df3-45cc-abc0-ffa837cca5d8%2F084ad027-1e11-47fd-966c-9fa631305284%2Ftxio5fa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine whether the following matrices are linearly independent or linearly dependent in \( M_{22} \).
\[ m_1 = \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}, \quad m_2 = \begin{bmatrix} 2 & 3 \\ 4 & 0 \end{bmatrix}, \quad m_3 = \begin{bmatrix} 0 & 1 \\ -1 & 5 \end{bmatrix}, \quad m_4 = \begin{bmatrix} 2 & 0 \\ 1 & -3 \end{bmatrix} \]
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