Define non-trivial solution.
Understand the Problem
The question is asking for a definition of a non-trivial solution, typically in the context of mathematics and problem-solving. A non-trivial solution refers to a solution that is not immediately obvious or simplistic, often implying that there are more complex or less obvious solutions that still fulfill the requirements of a given problem.
Answer
A solution where at least one variable is not zero.
The final answer is a solution where at least one variable is not zero.
Answer for screen readers
The final answer is a solution where at least one variable is not zero.
More Information
A non-trivial solution is significant because it represents solutions other than the obvious zero solution, adding depth to problem-solving in mathematics.
Tips
Common mistakes include confusing trivial solutions (where all variables equal zero) with non-trivial solutions (where at least one variable is non-zero).
Sources
- What do trivial and non-trivial solution of homogeneous equations mean in matrices? - math.stackexchange.com
- Nontrivial - Mathwords - mathwords.com
- Nontrivial Definition & Meaning - Merriam-Webster - merriam-webster.com
