Perform the indicated operation when A = %3D -1 A?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Perform the indicated operation when \( A = \begin{bmatrix} 1 & 5 \\ 0 & -1 \end{bmatrix} \).
\[ A^2 \]
This includes matrix multiplication of \( A \times A \).
To find \( A^2 \), multiply the matrix \( A \) by itself:
Given:
\[ A = \begin{bmatrix} 1 & 5 \\ 0 & -1 \end{bmatrix} \]
The resulting expressions are as follows, with arrows indicating operations:
1. Multiply the first row by the first column:
\[ a_{11} = (1 \times 1) + (5 \times 0) \]
2. Multiply the first row by the second column:
\[ a_{12} = (1 \times 5) + (5 \times -1) \]
3. Multiply the second row by the first column:
\[ a_{21} = (0 \times 1) + (-1 \times 0) \]
4. Multiply the second row by the second column:
\[ a_{22} = (0 \times 5) + (-1 \times -1) \]
Place each result in the appropriate position within the 2x2 matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a7c37e1-d117-46e5-8cc2-cb36983cacd6%2Fe8757d8e-5736-4c9f-925d-e0e3120a61a2%2Fxyp0yx_processed.png&w=3840&q=75)
Transcribed Image Text:Perform the indicated operation when \( A = \begin{bmatrix} 1 & 5 \\ 0 & -1 \end{bmatrix} \).
\[ A^2 \]
This includes matrix multiplication of \( A \times A \).
To find \( A^2 \), multiply the matrix \( A \) by itself:
Given:
\[ A = \begin{bmatrix} 1 & 5 \\ 0 & -1 \end{bmatrix} \]
The resulting expressions are as follows, with arrows indicating operations:
1. Multiply the first row by the first column:
\[ a_{11} = (1 \times 1) + (5 \times 0) \]
2. Multiply the first row by the second column:
\[ a_{12} = (1 \times 5) + (5 \times -1) \]
3. Multiply the second row by the first column:
\[ a_{21} = (0 \times 1) + (-1 \times 0) \]
4. Multiply the second row by the second column:
\[ a_{22} = (0 \times 5) + (-1 \times -1) \]
Place each result in the appropriate position within the 2x2 matrix.
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