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For the following set of linear equations, x₁ + 2x₂ + x₃ = 3 2x₁ + 3x₂ + x₃ = 3 3x₁ + 5x₂ + 2x₃ = 1 what can be said about the solution set?

1. There are exactly three solutions.
2. There is one and only one solution.
3. The equations are inconsistent, so no solution exists.
4. There are infinitely many solutions.

Correct answer: The equations are inconsistent, so no solution exists.

Solution

The equations are inconsistent because they do not intersect at any point in space, indicating that there is no set of values for the variables that satisfies all three equations simultaneously.

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