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
Related questions
Question
18
![**Title: Using Row Operations to Reduce a Matrix**
---
**Instructions:**
Perform row operations to reduce the following matrix to its reduced form.
**Given Matrix:**
\[
\begin{bmatrix}
1 & 1 & 1 & \vert & 18 \\
3 & 4 & 5 & \vert & 28 \\
\end{bmatrix}
\]
**Step-by-Step Solution:**
1. **Original Augmented Matrix:**
\[
\begin{bmatrix}
1 & 1 & 1 & \vert & 18 \\
3 & 4 & 5 & \vert & 28 \\
\end{bmatrix}
\]
2. **Apply Row Operations:**
Let \(\sim\) indicate that we perform row operations to transform the matrix.
\[
\begin{bmatrix}
1 & 1 & 1 & \vert & 18 \\
3 & 4 & 5 & \vert & 28 \\
\end{bmatrix}
\]
\[
\sim
\begin{bmatrix}
\boxed{\phantom{0}} & \boxed{\phantom{0}} & \boxed{\phantom{0}} & \vert & \boxed{\phantom{0}} \\
\boxed{\phantom{0}} & \boxed{\phantom{0}} & \boxed{\phantom{0}} & \vert & \boxed{\phantom{0}} \\
\end{bmatrix}
\]
**Note:** Fill in the boxed elements as you perform the row operations to achieve the reduced row-echelon form (RREF) or any simplified form as required.
The goal is to create leading ones and zeros in appropriate positions to simplify the matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d9df1eb-9cbe-4888-87d6-c14249115dd3%2Fd39cd26b-6308-491d-958a-c7ab8f40858d%2Fvl17p5_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Using Row Operations to Reduce a Matrix**
---
**Instructions:**
Perform row operations to reduce the following matrix to its reduced form.
**Given Matrix:**
\[
\begin{bmatrix}
1 & 1 & 1 & \vert & 18 \\
3 & 4 & 5 & \vert & 28 \\
\end{bmatrix}
\]
**Step-by-Step Solution:**
1. **Original Augmented Matrix:**
\[
\begin{bmatrix}
1 & 1 & 1 & \vert & 18 \\
3 & 4 & 5 & \vert & 28 \\
\end{bmatrix}
\]
2. **Apply Row Operations:**
Let \(\sim\) indicate that we perform row operations to transform the matrix.
\[
\begin{bmatrix}
1 & 1 & 1 & \vert & 18 \\
3 & 4 & 5 & \vert & 28 \\
\end{bmatrix}
\]
\[
\sim
\begin{bmatrix}
\boxed{\phantom{0}} & \boxed{\phantom{0}} & \boxed{\phantom{0}} & \vert & \boxed{\phantom{0}} \\
\boxed{\phantom{0}} & \boxed{\phantom{0}} & \boxed{\phantom{0}} & \vert & \boxed{\phantom{0}} \\
\end{bmatrix}
\]
**Note:** Fill in the boxed elements as you perform the row operations to achieve the reduced row-echelon form (RREF) or any simplified form as required.
The goal is to create leading ones and zeros in appropriate positions to simplify the matrix.
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