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-4 8 1 2 1 2 3 8 Let A 2 4 -3 10 9 3 6 0 6 9 1. Find a basis for Col A, and give a non-zero vector in Col A. 2. We learned that for any matrix B, Col B is always a subspace of a vector space. What vector space is Col A a subspace of? 3. Find a basis for Nul A, and give a non-zero vector in Nul A.

-4 8 1 2 1 2 3 8 Let A 2 4 -3 10 9 3 6 0 6 9 1. Find a basis for Col A, and give a non-zero vector in Col A. 2. We learned that for any matrix B, Col B is always a subspace of a vector space. What vector space is Col A a subspace of? 3. Find a basis for Nul A, and give a non-zero vector in Nul A.

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
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Let \( A = \begin{bmatrix} 1 & 2 & 3 & -4 & 8 \\ 1 & 2 & 0 & 2 & 8 \\ 2 & 4 & -3 & 10 & 9 \\ 3 & 6 & 0 & 6 & 9 \end{bmatrix} \). 1. Find a basis for \(\text{Col } A\), and give a non-zero vector in \(\text{Col } A\). 2. We learned that for any matrix \( B \), \(\text{Col } B\) is always a subspace of a vector space. What vector space is \(\text{Col } A\) a subspace of? 3. Find a basis for \(\text{Nul } A\), and give a non-zero vector in \(\text{Nul } A\). 4. We learned that for any matrix \( B \), \(\text{Nul } B\) is always a subspace of a vector space. What vector space is \(\text{Nul } A\) a subspace of?
Transcribed Image Text:Let \( A = \begin{bmatrix} 1 & 2 & 3 & -4 & 8 \\ 1 & 2 & 0 & 2 & 8 \\ 2 & 4 & -3 & 10 & 9 \\ 3 & 6 & 0 & 6 & 9 \end{bmatrix} \). 1. Find a basis for \(\text{Col } A\), and give a non-zero vector in \(\text{Col } A\). 2. We learned that for any matrix \( B \), \(\text{Col } B\) is always a subspace of a vector space. What vector space is \(\text{Col } A\) a subspace of? 3. Find a basis for \(\text{Nul } A\), and give a non-zero vector in \(\text{Nul } A\). 4. We learned that for any matrix \( B \), \(\text{Nul } B\) is always a subspace of a vector space. What vector space is \(\text{Nul } A\) a subspace of?
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