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The system of linear equations 3x − 2y − kz = 10 2x − 4y − 2z = 6 x + 2y − z = 5m is inconsistent if : (1) k = 3, m = 4/5 (2) k ≠ 3, m ∈ R (3) k ≠ 3, m ≠ 4/5 (4) k = 3, m ≠ 4/5

1. k = 3, m = 4/5
2. k ≠ 3, m ∈ R
3. k ≠ 3, m ≠ 4/5
4. k = 3, m ≠ 4/5

Correct answer: k ≠ 3, m ≠ 4/5

Solution

The system is inconsistent when the equations do not have a common solution, which occurs when the parameters k and m take values that prevent the equations from intersecting. Specifically, if k is not equal to 3 and m is not equal to 4/5, the equations diverge enough to ensure no solution exists.

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