In Exercises 3-4, find a row operation and the corresponding ele- mentary matrix that will restore the given elementary matrix to the identity matrix. 7. -7 0 0 1 b. 0 1 0 3. a. 0 0 0 1 0 1 01 00 C. 00 0 0 10 0 01 0 -5 01 d. - 0 0 1 1 0 8
In Exercises 3-4, find a row operation and the corresponding ele- mentary matrix that will restore the given elementary matrix to the identity matrix. 7. -7 0 0 1 b. 0 1 0 3. a. 0 0 0 1 0 1 01 00 C. 00 0 0 10 0 01 0 -5 01 d. - 0 0 1 1 0 8
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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F1.5 question 3 on paper please
![### Elementary Matrices and Row Operations
This section focuses on understanding elementary matrices and their corresponding row operations. Below are exercises designed to restore given elementary matrices to the identity matrix and to apply row operations to given matrices.
#### Exercise 2
For this exercise, identify if the given matrices are elementary matrices.
a.
\[
\begin{bmatrix}
1 & 0 \\
0 & \sqrt{3}
\end{bmatrix}
\]
b.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
-1 & 0 & 1
\end{bmatrix}
\]
c.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\]
d.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 0 & 1 \\
0 & 1 & 0
\end{bmatrix}
\]
#### Exercise 3
In Exercises 3–4, find a row operation and the corresponding element matrix that will restore the given elementary matrix to the identity matrix.
a.
\[
\begin{bmatrix}
1 & -3 \\
0 & 1
\end{bmatrix}
\]
b.
\[
\begin{bmatrix}
-7 & 0 \\
0 & 1
\end{bmatrix}
\]
c.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
1 & 0 & 0
\end{bmatrix}
\]
d.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 7
\end{bmatrix}
\]
#### Exercise 4
Continue restoring the elementary matrices to the identity matrix.
a.
\[
\begin{bmatrix}
1 & 0 \\
-3 & 1
\end{bmatrix}
\]
b.
\[
\begin{bmatrix}
0 & 1 & 0 & 0 \\
1 & 0 & 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccdd90b5-cd41-4340-8a36-15b102c9ba73%2F92747dc1-2584-4ab4-9d84-d049949f6baf%2Fpsh38ll_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Elementary Matrices and Row Operations
This section focuses on understanding elementary matrices and their corresponding row operations. Below are exercises designed to restore given elementary matrices to the identity matrix and to apply row operations to given matrices.
#### Exercise 2
For this exercise, identify if the given matrices are elementary matrices.
a.
\[
\begin{bmatrix}
1 & 0 \\
0 & \sqrt{3}
\end{bmatrix}
\]
b.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
-1 & 0 & 1
\end{bmatrix}
\]
c.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\]
d.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 0 & 1 \\
0 & 1 & 0
\end{bmatrix}
\]
#### Exercise 3
In Exercises 3–4, find a row operation and the corresponding element matrix that will restore the given elementary matrix to the identity matrix.
a.
\[
\begin{bmatrix}
1 & -3 \\
0 & 1
\end{bmatrix}
\]
b.
\[
\begin{bmatrix}
-7 & 0 \\
0 & 1
\end{bmatrix}
\]
c.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
1 & 0 & 0
\end{bmatrix}
\]
d.
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 7
\end{bmatrix}
\]
#### Exercise 4
Continue restoring the elementary matrices to the identity matrix.
a.
\[
\begin{bmatrix}
1 & 0 \\
-3 & 1
\end{bmatrix}
\]
b.
\[
\begin{bmatrix}
0 & 1 & 0 & 0 \\
1 & 0 & 0
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