**Finding the Inverse of a Matrix** In Exercises 7–18, find the inverse of the matrix, if it exists. 7. \[ \begin{bmatrix} 2 & 3 \\ 1 & 2 \\ \end{bmatrix} \] 8. \[ \begin{bmatrix} 1 & 2 \\ 1 & 3 \\ \end{bmatrix} \] 9. \[ \begin{bmatrix} 1 & 2 \\ 2 & 4 \\ \end{bmatrix} \] 10. \[ \begin{bmatrix} 2 & -3 \\ 1 & -1 \\ \end{bmatrix} \] 11. \[ \begin{bmatrix} 1 & 2 \\ 4 & 10 \\ \end{bmatrix} \] 12. \[ \begin{bmatrix} 2 & -2 \\ 2 & -1 \\ \end{bmatrix} \] 13. \[ \begin{bmatrix} 1 & 5 & 4 \\ 1 & 6 & 5 \\ 1 & 7 & 6 \\ \end{bmatrix} \] 14. \[ \begin{bmatrix} 3 & 2 & 0 \\ 2 & 3 & 0 \\ 0 & 0 & 6 \\ \end{bmatrix} \] 15. \[ \begin{bmatrix} 1 & 2 & 4 \\ 1 & 3 & 6 \\ 1 & 2 & 5 \\ \end{bmatrix} \] 16. \[ \begin{bmatrix} 2 & 4 & 1 \\ 3 & 6 & 1 \\ 2 & 4 & 2 \\ \end{bmatrix} \] 17. \[ \begin{bmatrix} 2 & 1 & 1 \\ 5 & 2 & 1 \\ 3 & 2 & 1 \\ \end{bmatrix} \] 18. \[ \begin{bmatrix} 5 & 2 & 1 \\ 4 & 2 & 1 \\ 2 & 1 & 0 \\ \end{bmatrix} \]
**Finding the Inverse of a Matrix** In Exercises 7–18, find the inverse of the matrix, if it exists. 7. \[ \begin{bmatrix} 2 & 3 \\ 1 & 2 \\ \end{bmatrix} \] 8. \[ \begin{bmatrix} 1 & 2 \\ 1 & 3 \\ \end{bmatrix} \] 9. \[ \begin{bmatrix} 1 & 2 \\ 2 & 4 \\ \end{bmatrix} \] 10. \[ \begin{bmatrix} 2 & -3 \\ 1 & -1 \\ \end{bmatrix} \] 11. \[ \begin{bmatrix} 1 & 2 \\ 4 & 10 \\ \end{bmatrix} \] 12. \[ \begin{bmatrix} 2 & -2 \\ 2 & -1 \\ \end{bmatrix} \] 13. \[ \begin{bmatrix} 1 & 5 & 4 \\ 1 & 6 & 5 \\ 1 & 7 & 6 \\ \end{bmatrix} \] 14. \[ \begin{bmatrix} 3 & 2 & 0 \\ 2 & 3 & 0 \\ 0 & 0 & 6 \\ \end{bmatrix} \] 15. \[ \begin{bmatrix} 1 & 2 & 4 \\ 1 & 3 & 6 \\ 1 & 2 & 5 \\ \end{bmatrix} \] 16. \[ \begin{bmatrix} 2 & 4 & 1 \\ 3 & 6 & 1 \\ 2 & 4 & 2 \\ \end{bmatrix} \] 17. \[ \begin{bmatrix} 2 & 1 & 1 \\ 5 & 2 & 1 \\ 3 & 2 & 1 \\ \end{bmatrix} \] 18. \[ \begin{bmatrix} 5 & 2 & 1 \\ 4 & 2 & 1 \\ 2 & 1 & 0 \\ \end{bmatrix} \]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
#17
![**Finding the Inverse of a Matrix**
In Exercises 7–18, find the inverse of the matrix, if it exists.
7.
\[
\begin{bmatrix}
2 & 3 \\
1 & 2 \\
\end{bmatrix}
\]
8.
\[
\begin{bmatrix}
1 & 2 \\
1 & 3 \\
\end{bmatrix}
\]
9.
\[
\begin{bmatrix}
1 & 2 \\
2 & 4 \\
\end{bmatrix}
\]
10.
\[
\begin{bmatrix}
2 & -3 \\
1 & -1 \\
\end{bmatrix}
\]
11.
\[
\begin{bmatrix}
1 & 2 \\
4 & 10 \\
\end{bmatrix}
\]
12.
\[
\begin{bmatrix}
2 & -2 \\
2 & -1 \\
\end{bmatrix}
\]
13.
\[
\begin{bmatrix}
1 & 5 & 4 \\
1 & 6 & 5 \\
1 & 7 & 6 \\
\end{bmatrix}
\]
14.
\[
\begin{bmatrix}
3 & 2 & 0 \\
2 & 3 & 0 \\
0 & 0 & 6 \\
\end{bmatrix}
\]
15.
\[
\begin{bmatrix}
1 & 2 & 4 \\
1 & 3 & 6 \\
1 & 2 & 5 \\
\end{bmatrix}
\]
16.
\[
\begin{bmatrix}
2 & 4 & 1 \\
3 & 6 & 1 \\
2 & 4 & 2 \\
\end{bmatrix}
\]
17.
\[
\begin{bmatrix}
2 & 1 & 1 \\
5 & 2 & 1 \\
3 & 2 & 1 \\
\end{bmatrix}
\]
18.
\[
\begin{bmatrix}
5 & 2 & 1 \\
4 & 2 & 1 \\
2 & 1 & 0 \\
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F215c9956-76b8-4988-9874-46d947288784%2F81cfe41a-3df5-4101-aeb0-ca38815ade9a%2Fxq6wzja_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Inverse of a Matrix**
In Exercises 7–18, find the inverse of the matrix, if it exists.
7.
\[
\begin{bmatrix}
2 & 3 \\
1 & 2 \\
\end{bmatrix}
\]
8.
\[
\begin{bmatrix}
1 & 2 \\
1 & 3 \\
\end{bmatrix}
\]
9.
\[
\begin{bmatrix}
1 & 2 \\
2 & 4 \\
\end{bmatrix}
\]
10.
\[
\begin{bmatrix}
2 & -3 \\
1 & -1 \\
\end{bmatrix}
\]
11.
\[
\begin{bmatrix}
1 & 2 \\
4 & 10 \\
\end{bmatrix}
\]
12.
\[
\begin{bmatrix}
2 & -2 \\
2 & -1 \\
\end{bmatrix}
\]
13.
\[
\begin{bmatrix}
1 & 5 & 4 \\
1 & 6 & 5 \\
1 & 7 & 6 \\
\end{bmatrix}
\]
14.
\[
\begin{bmatrix}
3 & 2 & 0 \\
2 & 3 & 0 \\
0 & 0 & 6 \\
\end{bmatrix}
\]
15.
\[
\begin{bmatrix}
1 & 2 & 4 \\
1 & 3 & 6 \\
1 & 2 & 5 \\
\end{bmatrix}
\]
16.
\[
\begin{bmatrix}
2 & 4 & 1 \\
3 & 6 & 1 \\
2 & 4 & 2 \\
\end{bmatrix}
\]
17.
\[
\begin{bmatrix}
2 & 1 & 1 \\
5 & 2 & 1 \\
3 & 2 & 1 \\
\end{bmatrix}
\]
18.
\[
\begin{bmatrix}
5 & 2 & 1 \\
4 & 2 & 1 \\
2 & 1 & 0 \\
\end{bmatrix}
\]
Expert Solution
Step 1
17.
The given matrix is
The inverse of the above matrix will exists if .
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
