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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![### Computing the Inverse of Matrices Using Theorem 1.4.5
In Exercises **5–8**, use **Theorem 1.4.5** to compute the inverse of the matrix.
#### 5. Matrix A
\[
A = \begin{bmatrix}
2 & -3 \\
4 & 4
\end{bmatrix}
\]
#### 6. Matrix B
\[
B = \begin{bmatrix}
3 & 1 \\
5 & 2
\end{bmatrix}
\]
#### 7. Matrix C
\[
C = \begin{bmatrix}
2 & 0 \\
0 & 3
\end{bmatrix}
\]
#### 8. Matrix D
\[
D = \begin{bmatrix}
6 & 4 \\
-2 & -1
\end{bmatrix}
\]
**Explanation:**
- Each matrix shown is a 2x2 matrix.
- The goal is to compute the inverse of each matrix using Theorem 1.4.5, which provides a method for finding the inverse of a 2x2 matrix, typically involving the determinant and the adjugate of the matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcabf4e2-d726-470f-ab0b-ceee8041df2c%2Fc96d9a7c-22f4-4ef6-bfa2-338ffc266634%2F75r5stp_processed.png&w=3840&q=75)
Transcribed Image Text:### Computing the Inverse of Matrices Using Theorem 1.4.5
In Exercises **5–8**, use **Theorem 1.4.5** to compute the inverse of the matrix.
#### 5. Matrix A
\[
A = \begin{bmatrix}
2 & -3 \\
4 & 4
\end{bmatrix}
\]
#### 6. Matrix B
\[
B = \begin{bmatrix}
3 & 1 \\
5 & 2
\end{bmatrix}
\]
#### 7. Matrix C
\[
C = \begin{bmatrix}
2 & 0 \\
0 & 3
\end{bmatrix}
\]
#### 8. Matrix D
\[
D = \begin{bmatrix}
6 & 4 \\
-2 & -1
\end{bmatrix}
\]
**Explanation:**
- Each matrix shown is a 2x2 matrix.
- The goal is to compute the inverse of each matrix using Theorem 1.4.5, which provides a method for finding the inverse of a 2x2 matrix, typically involving the determinant and the adjugate of the matrix.
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