3 13. In Exercises 11-16,compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.
3 13. In Exercises 11-16,compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.
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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![**Exercise 13**
\[
\begin{bmatrix}
3 & 5 & 4 \\
1 & 0 & 1 \\
2 & 1 & 1
\end{bmatrix}
\]
---
In Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1a8ba3-371b-48d7-95b6-c118f740fa83%2Ff4c3aae2-8a8c-44fe-9487-2a885804e028%2F9dxhv3_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise 13**
\[
\begin{bmatrix}
3 & 5 & 4 \\
1 & 0 & 1 \\
2 & 1 & 1
\end{bmatrix}
\]
---
In Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.
![## Theorem 8: An Inverse Formula
Let \( A \) be an invertible \( n \times n \) matrix. Then
\[ A^{-1} = \frac{1}{\det A} \text{adj } A \]
Where:
- \( A^{-1} \) is the inverse of matrix \( A \).
- \( \det A \) is the determinant of matrix \( A \).
- \( \text{adj } A \) is the adjugate (or adjoint) of matrix \( A \).
This theorem provides a formula to compute the inverse of an invertible matrix using its determinant and its adjugate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1a8ba3-371b-48d7-95b6-c118f740fa83%2Ff4c3aae2-8a8c-44fe-9487-2a885804e028%2Ft57edn_processed.png&w=3840&q=75)
Transcribed Image Text:## Theorem 8: An Inverse Formula
Let \( A \) be an invertible \( n \times n \) matrix. Then
\[ A^{-1} = \frac{1}{\det A} \text{adj } A \]
Where:
- \( A^{-1} \) is the inverse of matrix \( A \).
- \( \det A \) is the determinant of matrix \( A \).
- \( \text{adj } A \) is the adjugate (or adjoint) of matrix \( A \).
This theorem provides a formula to compute the inverse of an invertible matrix using its determinant and its adjugate.
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