Use the row reduction algorithm to transform the matrix into reduced echelon form. 1 4 - 5 1 2 -4 -1 4 - 3 -9 9 2 8 O A. 30 23 O B. 10 0 0 23 10 0 1 -2 0 - 7 0 100 -7 0 0 0 1 7 0 0 0 1 7 Oc. 1 4 -5 0 -5 OD. 1 4 -5 1 2 0 1 -20 - 7 0 1 -2 10 0 0 0 1 7 0 1 7
Use the row reduction algorithm to transform the matrix into reduced echelon form. 1 4 - 5 1 2 -4 -1 4 - 3 -9 9 2 8 O A. 30 23 O B. 10 0 0 23 10 0 1 -2 0 - 7 0 100 -7 0 0 0 1 7 0 0 0 1 7 Oc. 1 4 -5 0 -5 OD. 1 4 -5 1 2 0 1 -20 - 7 0 1 -2 10 0 0 0 1 7 0 1 7
Algebra and Trigonometry (6th Edition)
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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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![### Row Reduction to Reduced Echelon Form
To transform the given matrix into reduced row echelon form, we use the row reduction algorithm. The original matrix is:
\[
\begin{bmatrix}
1 & 4 & -5 & 1 & 2 \\
2 & 5 & -4 & 1 & 4 \\
-3 & -9 & 9 & 2 & 8
\end{bmatrix}
\]
Below are the multiple-choice options representing different stages that could be achieved through the row reduction algorithm:
**Option A:**
\[
\begin{bmatrix}
1 & 0 & 3 & 0 & 23 \\
0 & 1 & -2 & 0 & -7 \\
0 & 0 & 0 & 1 & 7
\end{bmatrix}
\]
**Option B:**
\[
\begin{bmatrix}
1 & 0 & 0 & 0 & 23 \\
0 & 1 & 0 & 0 & -7 \\
0 & 0 & 0 & 1 & 7
\end{bmatrix}
\]
**Option C:**
\[
\begin{bmatrix}
1 & 4 & -5 & 0 & -5 \\
0 & 1 & -2 & 0 & -7 \\
0 & 0 & 0 & 1 & 7
\end{bmatrix}
\]
**Option D:**
\[
\begin{bmatrix}
1 & 4 & -5 & 1 & 2 \\
0 & 1 & -2 & 1 & 0 \\
0 & 0 & 0 & 1 & 7
\end{bmatrix}
\]
The task is to identify which of these options represent the correct reduced echelon form of the matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda2e0952-5073-44c4-aa37-c19a81cec12c%2Fc2c65dd0-f69d-4aca-81f1-ecbcb3d4a371%2Fay7uhz9_processed.png&w=3840&q=75)
Transcribed Image Text:### Row Reduction to Reduced Echelon Form
To transform the given matrix into reduced row echelon form, we use the row reduction algorithm. The original matrix is:
\[
\begin{bmatrix}
1 & 4 & -5 & 1 & 2 \\
2 & 5 & -4 & 1 & 4 \\
-3 & -9 & 9 & 2 & 8
\end{bmatrix}
\]
Below are the multiple-choice options representing different stages that could be achieved through the row reduction algorithm:
**Option A:**
\[
\begin{bmatrix}
1 & 0 & 3 & 0 & 23 \\
0 & 1 & -2 & 0 & -7 \\
0 & 0 & 0 & 1 & 7
\end{bmatrix}
\]
**Option B:**
\[
\begin{bmatrix}
1 & 0 & 0 & 0 & 23 \\
0 & 1 & 0 & 0 & -7 \\
0 & 0 & 0 & 1 & 7
\end{bmatrix}
\]
**Option C:**
\[
\begin{bmatrix}
1 & 4 & -5 & 0 & -5 \\
0 & 1 & -2 & 0 & -7 \\
0 & 0 & 0 & 1 & 7
\end{bmatrix}
\]
**Option D:**
\[
\begin{bmatrix}
1 & 4 & -5 & 1 & 2 \\
0 & 1 & -2 & 1 & 0 \\
0 & 0 & 0 & 1 & 7
\end{bmatrix}
\]
The task is to identify which of these options represent the correct reduced echelon form of the matrix.
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