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Consider the system of linear equations: lambda*x + 2y + 2z = 5; 2*lambda*x + 3y + 5z = 8; 4x + lambda*y + 6z = 10. Which of the following statements is correct?

1. infinitely many solutions when lambda = 2
2. a unique solution when lambda = -8
3. no solution when lambda = 8
4. no solution when lambda = 2

Correct answer: no solution when lambda = 2

Solution

The determinant vanishes at lambda = 2 and lambda = -8; at lambda = 2 the augmented matrix has higher rank than the coefficient matrix, so the system has no solution.

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