What is a non-trivial solution in linear algebra?
Understand the Problem
The question is asking for an explanation of what constitutes a non-trivial solution in the context of linear algebra. A non-trivial solution typically refers to solutions of a system of equations that are not obvious or simplistic, often meaning that the solution is not just the zero vector.
Answer
Any solution that is not the zero vector.
A non-trivial solution in linear algebra is any solution to a homogeneous system of equations that is not the zero vector.
Answer for screen readers
A non-trivial solution in linear algebra is any solution to a homogeneous system of equations that is not the zero vector.
More Information
A homogeneous linear system has a non-trivial solution if it has infinitely many solutions or is underdetermined.
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