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Let the system of linear equations x + y + az = 2 3x + y + z = 4 x + 2z = 1 have a unique solution (x*, y*, z*). If (α, x*), (y*, α) and (x*, -y*) are collinear points, then the sum of absolute values of all possible values of α is

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

Correct answer: 2

Solution

The system of equations must have a unique solution, which implies that the determinant of the coefficient matrix is non-zero. The collinearity condition for the points given leads to a specific relationship involving α, which can be solved to yield possible values of α that sum to 2 in absolute value.

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