Which one of the following is NOT a basic solution of the system of linear equations
x₁ + 2x₂ + x₃ = 4
2x₁ + x₂ + 5x₃ = 5
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: A. x₁ = −1, x₂ = 2, x₃ = 1
Explanation
With 2 equations and 3 variables, a basic solution sets 3 − 2 = 1 variable to zero and solves for the other two. Options B, C and D each have one variable zero and satisfy both equations. Option A also satisfies both equations, but no variable is zero, so it is a solution but not a basic solution.More Discrete Structures and Optimization questions
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