Find the inverse of each of the following elementary matrices: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix 1 0 0 0 -1 0-300 0010 001 Гоо о 11-1 Го о о = 000 000
Find the inverse of each of the following elementary matrices: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix 1 0 0 0 -1 0-300 0010 001 Гоо о 11-1 Го о о = 000 000
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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Question
![Find the inverse of each of the following elementary matrices:
You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix.
1. \[
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & -3 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{bmatrix}^{-1}
=
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
2. \[
\begin{bmatrix}
0 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
1 & 0 & 0 & 0 \\
\end{bmatrix}^{-1}
=
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
3. \[
\begin{bmatrix}
1 & 0 & 0 & 0 \\
-2 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{bmatrix}^{-1}
=
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86b14285-d986-492a-886d-db2235fe87ed%2F3fb35f77-3968-4f71-8f58-35f0fd0e3b93%2Fojwhq7n_processed.png&w=3840&q=75)
Transcribed Image Text:Find the inverse of each of the following elementary matrices:
You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix.
1. \[
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & -3 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{bmatrix}^{-1}
=
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
2. \[
\begin{bmatrix}
0 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
1 & 0 & 0 & 0 \\
\end{bmatrix}^{-1}
=
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
3. \[
\begin{bmatrix}
1 & 0 & 0 & 0 \\
-2 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{bmatrix}^{-1}
=
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
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