Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.3: Matrix Approa To Solving Linear Systems
Problem 51PS
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![Below is the transcription of the displayed image intended for an educational website. The image includes text instructions and an augmented matrix alongside an empty grid for matrix manipulation. There is also a sidebar for submission and help options.
---
### Educational Exercise: Matrix Echelon Form
**Task:**
Find the echelon form of this augmented matrix, written so there are 1's on the diagonal.
**Given Matrix:**
\[
\begin{pmatrix}
1 & 2 & -2 & 100 \\
1 & 3 & 1 & 500 \\
-1 & 6 & 1 & 500
\end{pmatrix}
\]
Use the empty grid to perform row operations leading to the echelon form of the matrix.
---
**Instructions:**
1. **Identify Pivot Positions:**
- Ensure the leading coefficients (or pivots) are 1's on the diagonal of the matrix.
2. **Row Operations:**
- Perform the necessary row operations to convert the given matrix to its row echelon form.
3. **Goal:**
- Transform the matrix such that below each leading 1, all entries are zero.
**Submission:**
- After completing the transformation, click on the "Submit Question" button.
**Help Option:**
- For additional guidance, you may watch the tutorial by clicking on the "Video" link.
**Graphical Explanation:**
- The empty grid depicted is for manual entry of the steps taken during the matrix row operations, allowing you to visualize each intermediate step.
**Matrix Grid:**
\[
\begin{array}{cccc}
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\end{array}
\]
**Note:**
- Always double-check your row operations to ensure accuracy in each step towards achieving the row echelon form.
Happy Learning!
---
This transcription includes a detailed breakdown of the task, providing an educational context and guiding students through the process of converting a given matrix into its echelon form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5253470b-a88a-44a2-95c4-a44ae3e11575%2F305df6ba-d7b9-4387-bf6d-d291aaf449a7%2Fr8yy8db_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Below is the transcription of the displayed image intended for an educational website. The image includes text instructions and an augmented matrix alongside an empty grid for matrix manipulation. There is also a sidebar for submission and help options.
---
### Educational Exercise: Matrix Echelon Form
**Task:**
Find the echelon form of this augmented matrix, written so there are 1's on the diagonal.
**Given Matrix:**
\[
\begin{pmatrix}
1 & 2 & -2 & 100 \\
1 & 3 & 1 & 500 \\
-1 & 6 & 1 & 500
\end{pmatrix}
\]
Use the empty grid to perform row operations leading to the echelon form of the matrix.
---
**Instructions:**
1. **Identify Pivot Positions:**
- Ensure the leading coefficients (or pivots) are 1's on the diagonal of the matrix.
2. **Row Operations:**
- Perform the necessary row operations to convert the given matrix to its row echelon form.
3. **Goal:**
- Transform the matrix such that below each leading 1, all entries are zero.
**Submission:**
- After completing the transformation, click on the "Submit Question" button.
**Help Option:**
- For additional guidance, you may watch the tutorial by clicking on the "Video" link.
**Graphical Explanation:**
- The empty grid depicted is for manual entry of the steps taken during the matrix row operations, allowing you to visualize each intermediate step.
**Matrix Grid:**
\[
\begin{array}{cccc}
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} & \boxed{} \\
\end{array}
\]
**Note:**
- Always double-check your row operations to ensure accuracy in each step towards achieving the row echelon form.
Happy Learning!
---
This transcription includes a detailed breakdown of the task, providing an educational context and guiding students through the process of converting a given matrix into its echelon form.
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