Suppose that you're solving a matrix by hand, and you eventually get to the step listed below. What is the solution? If there is one answer, write it as an ordered pair. If there is no solution, state so. If there are infinitely many solutions, write your answer as an ordered pair and state which variable is arbitrary. (See pages 96-97 (videos 70–71)) (Answer: (fy, y),y is arbitrary OR (x, ¿x),xis arbitrary) [3 -4 0
Suppose that you're solving a matrix by hand, and you eventually get to the step listed below. What is the solution? If there is one answer, write it as an ordered pair. If there is no solution, state so. If there are infinitely many solutions, write your answer as an ordered pair and state which variable is arbitrary. (See pages 96-97 (videos 70–71)) (Answer: (fy, y),y is arbitrary OR (x, ¿x),xis arbitrary) [3 -4 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**1. Matrix Solution**
When solving a matrix by hand, you're given the following step:
\[
\begin{bmatrix}
3 & -4 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
What is the solution? If a solution exists, write it as an ordered pair. If no solution, state it. If there are infinitely many solutions, provide the answer as an ordered pair, indicating the arbitrary variable.
- **Answer:** \( (x, \frac{3}{4} x) \), \( x \) is arbitrary.
---
**2. Solving Systems of Equations with a Calculator**
**a. Solve the system:**
\[
\begin{align*}
-2x + 7y - 6z &= -9 \\
x - 2y - 3z &= 6 \\
z &= 5 - x + 3y
\end{align*}
\]
- **Answer:** \( (11z + 8, 4z + 1, z) \), \( z \) is arbitrary.
**b. Solve the system:**
\[
\begin{align*}
-2x + 3y &= 11z - 4 \\
x - 2y + 8z &= 6 \\
3z &= 3 - x + y
\end{align*}
\]
- **Answer:** No Solution / System is Inconsistent
**c. Solve the system:**
\[
\begin{align*}
2z &= 1 + 3x \\
x + 4z &= 3 - y \\
4x + y &= 3 + 2z
\end{align*}
\]
- **Answer:** \( (-0.5, 4.5, -0.25) \)
---
**3. Protein Supplements Data**
The table provides nutritional information for three protein supplements:
| | Protein (g) | Carbohydrates (g) | Sodium (mg) | Cost (\$) |
|--------------|-------------|-------------------|-------------|----------|
| Designer Whey| 18 | 2 | 80 | 0.50 |
| Muscle Milk | 32 | 16 | 240 | 1.60 |
| Pure Whey | 24 |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f2fc927-9fa0-46e3-98ea-45819a76f1ba%2F3a907859-9abf-46d4-9fd4-e3faa267e4e3%2Fok9syvg_processed.png&w=3840&q=75)
Transcribed Image Text:**1. Matrix Solution**
When solving a matrix by hand, you're given the following step:
\[
\begin{bmatrix}
3 & -4 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
What is the solution? If a solution exists, write it as an ordered pair. If no solution, state it. If there are infinitely many solutions, provide the answer as an ordered pair, indicating the arbitrary variable.
- **Answer:** \( (x, \frac{3}{4} x) \), \( x \) is arbitrary.
---
**2. Solving Systems of Equations with a Calculator**
**a. Solve the system:**
\[
\begin{align*}
-2x + 7y - 6z &= -9 \\
x - 2y - 3z &= 6 \\
z &= 5 - x + 3y
\end{align*}
\]
- **Answer:** \( (11z + 8, 4z + 1, z) \), \( z \) is arbitrary.
**b. Solve the system:**
\[
\begin{align*}
-2x + 3y &= 11z - 4 \\
x - 2y + 8z &= 6 \\
3z &= 3 - x + y
\end{align*}
\]
- **Answer:** No Solution / System is Inconsistent
**c. Solve the system:**
\[
\begin{align*}
2z &= 1 + 3x \\
x + 4z &= 3 - y \\
4x + y &= 3 + 2z
\end{align*}
\]
- **Answer:** \( (-0.5, 4.5, -0.25) \)
---
**3. Protein Supplements Data**
The table provides nutritional information for three protein supplements:
| | Protein (g) | Carbohydrates (g) | Sodium (mg) | Cost (\$) |
|--------------|-------------|-------------------|-------------|----------|
| Designer Whey| 18 | 2 | 80 | 0.50 |
| Muscle Milk | 32 | 16 | 240 | 1.60 |
| Pure Whey | 24 |
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