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A homogeneous system of equations −ax + y + z = 0 x − by + z = 0 x + y − cz = 0 where a, b, c ≠ −1, admits a non-trivial solution. Then the value of 1/(1+a) + 1/(1+b) + 1/(1+c) is:

1. 0
2. 1
3. 2
4. 3

Correct answer: 1

Solution

The system of equations has a non-trivial solution if the determinant of the coefficient matrix is zero. Given the conditions on a, b, and c, the relationship derived from the determinant leads to the conclusion that the sum of the fractions equals 1.

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