Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![Given the matrix \( A \):
\[
A = \begin{bmatrix}
-6 & 0 & 0 & 0 \\
0 & 8 & 0 & 0 \\
0 & 0 & -5 & 0 \\
0 & 0 & 0 & -7
\end{bmatrix}
\]
Then the inverse of the matrix \( A \), denoted as \( A^{-1} \), is represented by the empty structure:
\[
A^{-1} = \begin{bmatrix}
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{}
\end{bmatrix}
\]
Explanation:
- The matrix \( A \) is a diagonal matrix, meaning all the non-diagonal elements are zeros, and the diagonal elements can be inverted by taking their reciprocal (considering inverses of the values).
- The structure for \( A^{-1} \) is provided with empty boxes, indicating where the values should be filled in after calculating the inverse.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf673b33-84d3-4207-a3d8-77b439e8ab65%2F9acb99a1-e634-4d28-8290-c7ee61b97bb2%2Feh1r3w8_processed.png&w=3840&q=75)
Transcribed Image Text:Given the matrix \( A \):
\[
A = \begin{bmatrix}
-6 & 0 & 0 & 0 \\
0 & 8 & 0 & 0 \\
0 & 0 & -5 & 0 \\
0 & 0 & 0 & -7
\end{bmatrix}
\]
Then the inverse of the matrix \( A \), denoted as \( A^{-1} \), is represented by the empty structure:
\[
A^{-1} = \begin{bmatrix}
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{}
\end{bmatrix}
\]
Explanation:
- The matrix \( A \) is a diagonal matrix, meaning all the non-diagonal elements are zeros, and the diagonal elements can be inverted by taking their reciprocal (considering inverses of the values).
- The structure for \( A^{-1} \) is provided with empty boxes, indicating where the values should be filled in after calculating the inverse.
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