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:

• A. 1, -2
• B. 1, 2
• C. 1, -2
• D. 1, 2

Hint:

To solve systems of linear equations for consistency, check the determinant of the coefficient matrix and set it equal to zero.

Answer 1

The Correct Option is C

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.