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If the system of equations x + y + z = 6 x + 2y + 3z = 10 x + 2y + λz = 0 has a unique solution, then λ is not equal to

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

Correct answer: 3

Solution

For the system to have a unique solution, the determinant of the coefficient matrix must be non-zero. When λ equals 3, the rows of the matrix become linearly dependent, leading to a determinant of zero, which means the system does not have a unique solution.

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