Which of the following matrices is in reduced row echelon form? 1 0 -1 2 1 3 (A) 0 1 0 0 [1 02 5 (B) 0 1 -7 5 0 0 1 14 (C) 1 0 0 11 0 001 [₁ 1 0 -5 (D) 0 1 3 00 0
Which of the following matrices is in reduced row echelon form? 1 0 -1 2 1 3 (A) 0 1 0 0 [1 02 5 (B) 0 1 -7 5 0 0 1 14 (C) 1 0 0 11 0 001 [₁ 1 0 -5 (D) 0 1 3 00 0
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Question:**
Which of the following matrices is in *reduced row echelon form*?
**Matrices:**
(A)
\[
\begin{bmatrix}
1 & 0 & -1 & 1 \\
0 & 1 & 2 & 0 \\
0 & 1 & 3 & 1 \\
\end{bmatrix}
\]
(B)
\[
\begin{bmatrix}
1 & 0 & 2 & 5 \\
0 & 1 & -7 & 5 \\
0 & 0 & 1 & 14 \\
\end{bmatrix}
\]
(C)
\[
\begin{bmatrix}
1 & 0 & 0 & 11 & -3 \\
0 & 0 & 1 & 4 \\
\end{bmatrix}
\]
(D)
\[
\begin{bmatrix}
1 & 0 & -5 \\
0 & 1 & 3 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
**Options:**
- ○ A. A
- ○ B. B
- ○ C. C
- ○ D. D
**Explanation:**
The problem requires identifying which matrix is in reduced row echelon form (RREF). A matrix is in RREF if it satisfies the following conditions:
1. The leading entry of each nonzero row is 1.
2. Each leading 1 is the only nonzero entry in its column.
3. The leading 1 in any row is to the right of the leading 1 in the previous row.
4. Rows with all zeroes, if any, are at the bottom of the matrix.
Option (B) satisfies these conditions with a clear staircase pattern and leading 1s, and no nonzero entries elsewhere in their columns.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac0f3c56-5561-4b47-8ddf-f02546f51c3e%2F10ccbd17-ca42-47bb-8559-2b4a9719ccf6%2Fs6czdh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Which of the following matrices is in *reduced row echelon form*?
**Matrices:**
(A)
\[
\begin{bmatrix}
1 & 0 & -1 & 1 \\
0 & 1 & 2 & 0 \\
0 & 1 & 3 & 1 \\
\end{bmatrix}
\]
(B)
\[
\begin{bmatrix}
1 & 0 & 2 & 5 \\
0 & 1 & -7 & 5 \\
0 & 0 & 1 & 14 \\
\end{bmatrix}
\]
(C)
\[
\begin{bmatrix}
1 & 0 & 0 & 11 & -3 \\
0 & 0 & 1 & 4 \\
\end{bmatrix}
\]
(D)
\[
\begin{bmatrix}
1 & 0 & -5 \\
0 & 1 & 3 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
**Options:**
- ○ A. A
- ○ B. B
- ○ C. C
- ○ D. D
**Explanation:**
The problem requires identifying which matrix is in reduced row echelon form (RREF). A matrix is in RREF if it satisfies the following conditions:
1. The leading entry of each nonzero row is 1.
2. Each leading 1 is the only nonzero entry in its column.
3. The leading 1 in any row is to the right of the leading 1 in the previous row.
4. Rows with all zeroes, if any, are at the bottom of the matrix.
Option (B) satisfies these conditions with a clear staircase pattern and leading 1s, and no nonzero entries elsewhere in their columns.
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