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...
Related questions
Question
![**Problem Statement:**
**Objective:** Find the values of \( x \) and \( y \) that satisfy the following matrix equation.
**Matrix Equation:**
\[
\begin{bmatrix}
x + 2 & 2 & -7 \\
3 & 2y & 2x \\
5 & -6 & y + 2
\end{bmatrix}
=
\begin{bmatrix}
2x + 6 & 2 & -7 \\
3 & 14 & -8 \\
5 & -6 & 9
\end{bmatrix}
\]
**Solution:**
To find \( x \) and \( y \), equate corresponding elements of the matrices:
1. **First Row:**
- \( x + 2 = 2x + 6 \)
- \( 2 = 2 \) (Always true; no condition on variables)
- \( -7 = -7 \) (Always true; no condition on variables)
2. **Second Row:**
- \( 3 = 3 \) (Always true; no condition on variables)
- \( 2y = 14 \)
- \( 2x = -8 \)
3. **Third Row:**
- \( 5 = 5 \) (Always true; no condition on variables)
- \( -6 = -6 \) (Always true; no condition on variables)
- \( y + 2 = 9 \)
**Equations to Solve:**
- From the first row:
\[ x + 2 = 2x + 6 \]
- From the second row:
\[ 2y = 14 \]
\[ 2x = -8 \]
- From the third row:
\[ y + 2 = 9 \]
**Solutions:**
1. Solve for \( x \) from \( x + 2 = 2x + 6 \):
\[ x + 2 = 2x + 6 \]
\[ 2 = x + 6 \]
\[ x = -4 \]
2. Solve for \( y \) from \( 2y = 14 \):
\[ y = 7 \]
3. Verify \( y \) with \( y + 2 = 9 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fc3766d-bc8c-44dc-b95b-e319f0e06bc0%2F331c4267-75f5-4f09-bed9-c080e6756b9e%2Ffr0wrh6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
**Objective:** Find the values of \( x \) and \( y \) that satisfy the following matrix equation.
**Matrix Equation:**
\[
\begin{bmatrix}
x + 2 & 2 & -7 \\
3 & 2y & 2x \\
5 & -6 & y + 2
\end{bmatrix}
=
\begin{bmatrix}
2x + 6 & 2 & -7 \\
3 & 14 & -8 \\
5 & -6 & 9
\end{bmatrix}
\]
**Solution:**
To find \( x \) and \( y \), equate corresponding elements of the matrices:
1. **First Row:**
- \( x + 2 = 2x + 6 \)
- \( 2 = 2 \) (Always true; no condition on variables)
- \( -7 = -7 \) (Always true; no condition on variables)
2. **Second Row:**
- \( 3 = 3 \) (Always true; no condition on variables)
- \( 2y = 14 \)
- \( 2x = -8 \)
3. **Third Row:**
- \( 5 = 5 \) (Always true; no condition on variables)
- \( -6 = -6 \) (Always true; no condition on variables)
- \( y + 2 = 9 \)
**Equations to Solve:**
- From the first row:
\[ x + 2 = 2x + 6 \]
- From the second row:
\[ 2y = 14 \]
\[ 2x = -8 \]
- From the third row:
\[ y + 2 = 9 \]
**Solutions:**
1. Solve for \( x \) from \( x + 2 = 2x + 6 \):
\[ x + 2 = 2x + 6 \]
\[ 2 = x + 6 \]
\[ x = -4 \]
2. Solve for \( y \) from \( 2y = 14 \):
\[ y = 7 \]
3. Verify \( y \) with \( y + 2 = 9 \
Expert Solution
Step 1
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To find (x, y)
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