Suppose a traveler vacationed in France, Switzerland and Italy. The traveler spent a total of $300 for lodging, $375 for food and $390 for incidentals. The daily costs in France, Switzerland, and Italy, respectively, were $30, $20, $20 for lodging; $30, $25, and $30 for food and $30 in each country for incidentals. How many days did the traveler spend in each country? 1. Write the system of equations. Define each variable. 2. Write the coefficient matrix. 3. Write the augmented matrix for the system. 4. Solve the matrix using the Gauss-Jordan elimination method. 5. Write the matrix equation with the coefficient matrix, variable matrix and constant matrix. Identify each. 6. Find the inverse of the coefficient matrix. 7. Solve the system using the inverse matrix process. 8. Set up the four determinants for the system. 9. Use Cramer's Rule to solve the system. I

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Summary Problem: Systems of Linear Equations**

Suppose a traveler vacationed in France, Switzerland, and Italy. The traveler spent a total of $300 for lodging, $375 for food, and $390 for incidentals. The daily costs in France, Switzerland, and Italy, respectively, were $30, $20, $20 for lodging; $30, $25, and $30 for food; and $30 in each country for incidentals. How many days did the traveler spend in each country?

1. **Write the system of equations. Define each variable.**

2. **Write the coefficient matrix.**

3. **Write the augmented matrix for the system.**

4. **Solve the matrix using the Gauss-Jordan elimination method.**

5. **Write the matrix equation with the coefficient matrix, variable matrix, and constant matrix. Identify each.**

6. **Find the inverse of the coefficient matrix.**

7. **Solve the system using the inverse matrix process.**

8. **Set up the four determinants for the system.**

9. **Use Cramer's Rule to solve the system.**
Transcribed Image Text:**Summary Problem: Systems of Linear Equations** Suppose a traveler vacationed in France, Switzerland, and Italy. The traveler spent a total of $300 for lodging, $375 for food, and $390 for incidentals. The daily costs in France, Switzerland, and Italy, respectively, were $30, $20, $20 for lodging; $30, $25, and $30 for food; and $30 in each country for incidentals. How many days did the traveler spend in each country? 1. **Write the system of equations. Define each variable.** 2. **Write the coefficient matrix.** 3. **Write the augmented matrix for the system.** 4. **Solve the matrix using the Gauss-Jordan elimination method.** 5. **Write the matrix equation with the coefficient matrix, variable matrix, and constant matrix. Identify each.** 6. **Find the inverse of the coefficient matrix.** 7. **Solve the system using the inverse matrix process.** 8. **Set up the four determinants for the system.** 9. **Use Cramer's Rule to solve the system.**
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