I +1+2r3=-9 5z1+6z2-5z3= 5 %3D I3

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The image displays a set of mathematical problems and a system of linear equations. Here's the transcription and explanation:

On the left side of the image, there is a navigation section titled "Problems" with a list of problems numbered from 1 to 9. The user is currently hovering over "Problem 5."

In the center of the image, the following mathematical expression is displayed:

\[
\begin{bmatrix}
x_1 \\
x_2 \\
x_3
\end{bmatrix}
=
\begin{bmatrix}
\text{[ ]} \\
\text{[ ]} \\
\text{[ ]}
\end{bmatrix}
+
\begin{bmatrix}
\text{[ ]} \\
\text{[ ]} \\
\text{[ ]}
\end{bmatrix}
s
\]

To the right of this expression, there is a system of equations given as:

\[
\begin{cases}
x_1 + x_2 + 2x_3 = -9 \\
5x_1 + 6x_2 - 5x_3 = 5
\end{cases}
\]

Below these mathematical representations, there are two buttons labeled "Preview Answers" and "Submit Answers."

### Explanation:
- The matrix equation seems to represent a vector \( \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \) as the sum of two other vectors, possibly involving a parameter \( s \).
- The system of linear equations provides constraints or conditions based on which the values of \( x_1 \), \( x_2 \), and \( x_3 \) must be determined.

This content may be used as a practice exercise to solve systems of linear equations and understand vector representation in a linear algebra context.
Transcribed Image Text:The image displays a set of mathematical problems and a system of linear equations. Here's the transcription and explanation: On the left side of the image, there is a navigation section titled "Problems" with a list of problems numbered from 1 to 9. The user is currently hovering over "Problem 5." In the center of the image, the following mathematical expression is displayed: \[ \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} \text{[ ]} \\ \text{[ ]} \\ \text{[ ]} \end{bmatrix} + \begin{bmatrix} \text{[ ]} \\ \text{[ ]} \\ \text{[ ]} \end{bmatrix} s \] To the right of this expression, there is a system of equations given as: \[ \begin{cases} x_1 + x_2 + 2x_3 = -9 \\ 5x_1 + 6x_2 - 5x_3 = 5 \end{cases} \] Below these mathematical representations, there are two buttons labeled "Preview Answers" and "Submit Answers." ### Explanation: - The matrix equation seems to represent a vector \( \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \) as the sum of two other vectors, possibly involving a parameter \( s \). - The system of linear equations provides constraints or conditions based on which the values of \( x_1 \), \( x_2 \), and \( x_3 \) must be determined. This content may be used as a practice exercise to solve systems of linear equations and understand vector representation in a linear algebra context.
Expert Solution
Step 1

NOTE: Refresh your page if you can't see any equations.

.

system Ax=b is 

\begin{pmatrix}1&1&2\\ 5&6&-5\end{pmatrix}\begin{pmatrix}x_1\\ x_2\\ x_3\end{pmatrix}=\begin{pmatrix}-9\\ 5\end{pmatrix}

the augmented matrix is

\begin{pmatrix}1&1&2&-9\\ 5&6&-5&5\end{pmatrix}

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