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3 -2 4 that AB is the zero matrix. -6] 3. Let A = Find a 2 x 2 matrix B with two different nonzero columns such

3 -2 4 that AB is the zero matrix. -6] 3. Let A = Find a 2 x 2 matrix B with two different nonzero columns such

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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3. Let \( A = \begin{bmatrix} 3 & -6 \\ -2 & 4 \end{bmatrix} \). Find a \( 2 \times 2 \) matrix \( B \) with two different nonzero columns such that \( AB \) is the zero matrix. 4. If \( A = \begin{bmatrix} 1 & -3 \\ -3 & 5 \end{bmatrix} \) and \( AB = \begin{bmatrix} -3 & -11 \\ 1 & 17 \end{bmatrix} \), determine the first and second columns of \( B \). 5. Show that if the columns of \( B \) are linearly dependent, then so are the columns of \( AB \).
Transcribed Image Text:3. Let \( A = \begin{bmatrix} 3 & -6 \\ -2 & 4 \end{bmatrix} \). Find a \( 2 \times 2 \) matrix \( B \) with two different nonzero columns such that \( AB \) is the zero matrix. 4. If \( A = \begin{bmatrix} 1 & -3 \\ -3 & 5 \end{bmatrix} \) and \( AB = \begin{bmatrix} -3 & -11 \\ 1 & 17 \end{bmatrix} \), determine the first and second columns of \( B \). 5. Show that if the columns of \( B \) are linearly dependent, then so are the columns of \( AB \).
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