Matrix Echelon Tu 10-6 127 07 20 0 0 0 00 2143 6-127 0 1 O 02 00 Spans R² Spans R
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 82E
Related questions
Question
Please determine which echelon matrix span with a brief justification.
![The image contains handwritten notes organized into a table with three columns. The columns are labeled "Matrix Echelon Form," "Spans \( \mathbb{R}^2 \)," and "Spans \( \mathbb{R}^3 \)." Here is the transcription of the content:
**Matrix Echelon Form:**
1. First Matrix:
\[
\begin{bmatrix}
4 & 1 & 6 \\
0 & -6 & -1 \\
\end{bmatrix}
\]
2. Second Matrix:
\[
\begin{bmatrix}
1 & 2 & 7 \\
0 & 7 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
3. Third Matrix:
\[
\begin{bmatrix}
2 & 1 & 4 & 3 \\
0 & -1 & 2 & 7 \\
0 & 0 & 0 & 0 \\
\end{bmatrix}
\]
4. Fourth Matrix:
\[
\begin{bmatrix}
1 & 0 \\
0 & 2 \\
0 & 0 \\
\end{bmatrix}
\]
**Notes on Content Structure:**
- There are columns designated for "Spans \( \mathbb{R}^2 \)" and "Spans \( \mathbb{R}^3 \)" but these columns do not contain any content in the current image.
- Each matrix is presented in echelon form, which is a version often used to solve systems of linear equations and to determine properties like the rank of the matrix.
This structure suggests potential further analysis or discussion on whether the matrices span the respective vector spaces \( \mathbb{R}^2 \) and \( \mathbb{R}^3 \), though such details are not provided in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e996ea7-cb36-40c1-90ef-5b50ce800a3d%2F7bcec252-0704-43d2-aad2-fca705138c30%2Fdd5ea6c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains handwritten notes organized into a table with three columns. The columns are labeled "Matrix Echelon Form," "Spans \( \mathbb{R}^2 \)," and "Spans \( \mathbb{R}^3 \)." Here is the transcription of the content:
**Matrix Echelon Form:**
1. First Matrix:
\[
\begin{bmatrix}
4 & 1 & 6 \\
0 & -6 & -1 \\
\end{bmatrix}
\]
2. Second Matrix:
\[
\begin{bmatrix}
1 & 2 & 7 \\
0 & 7 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
3. Third Matrix:
\[
\begin{bmatrix}
2 & 1 & 4 & 3 \\
0 & -1 & 2 & 7 \\
0 & 0 & 0 & 0 \\
\end{bmatrix}
\]
4. Fourth Matrix:
\[
\begin{bmatrix}
1 & 0 \\
0 & 2 \\
0 & 0 \\
\end{bmatrix}
\]
**Notes on Content Structure:**
- There are columns designated for "Spans \( \mathbb{R}^2 \)" and "Spans \( \mathbb{R}^3 \)" but these columns do not contain any content in the current image.
- Each matrix is presented in echelon form, which is a version often used to solve systems of linear equations and to determine properties like the rank of the matrix.
This structure suggests potential further analysis or discussion on whether the matrices span the respective vector spaces \( \mathbb{R}^2 \) and \( \mathbb{R}^3 \), though such details are not provided in the image.
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