Solve by Cramer's rule:

2x-y + z=-1, x-2y + 3z = 4, 4x + y +2z = 4, solve this question without extra explaination

The solution to the system of equations using Cramer's rule is:

\[
x = -1, \quad y = 2, \quad z = 3
\]

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Here are 5 related questions to expand on this topic:
1. How is Cramer's rule derived for a 3x3 system?
2. What are the limitations of using Cramer's rule in solving systems of equations?
3. Can Cramer's rule be used for a system with infinite solutions?
4. How can determinants help in understanding the properties of linear systems?
5. What happens if the determinant of the coefficient matrix is zero?

**Tip:** Always check the determinant of the coefficient matrix before applying Cramer's rule—if it's zero, the system has no unique solution.

Solve by Cramer's rule: 2x - y + z = -1, x - 2y + 3z = 4, 4x + y + 2z = 4. Solve this question without extra explanation.

Learn how to solve a system of linear equations using Cramer's Rule. This example walks through solving the equations 2x - y + z = -1, x - 2y + 3z = 4, and 4x + y + 2z = 4, including calculating determinants and applying Cramer's Rule. Suitable for college-level linear algebra students.

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