Question:
The values of \( \alpha \) for which the system of equation \( x + y + z = 1 \), \( x + 2y + 4z = \alpha \), \( x + 4y + 10z = \alpha^2 \) is consistent are given by:
The values of \( \alpha \) for which the system of equation \( x + y + z = 1 \), \( x + 2y + 4z = \alpha \), \( x + 4y + 10z = \alpha^2 \) is consistent are given by:
Show Hint
To solve systems of linear equations for consistency, check the determinant of the coefficient matrix and set it equal to zero.
Updated On: Apr 27, 2026
- 1, -2
- 1, 2
- 1, -2
- 1, 2
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Solve the system.
The system of equations can be solved using the consistency condition, where the determinant of the coefficient matrix should be zero for the system to have a unique solution.
Step 2: Conclusion. Thus, the values of \( \alpha \) that make the system consistent are 1 and -2.
Step 2: Conclusion. Thus, the values of \( \alpha \) that make the system consistent are 1 and -2.
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