What is a trivial solution in linear algebra?
Understand the Problem
The question seeks to understand the concept of a trivial solution in linear algebra, which typically refers to the solution of a homogeneous linear system where all variables are set to zero.
Answer
X = 0
The final answer is X = 0
Answer for screen readers
The final answer is X = 0
More Information
In linear algebra, the trivial solution to a homogeneous system of linear equations (AX = 0) is when the vector X is the zero vector (all elements of X are zero). This solution is always present but may not be the only one.
Tips
Common mistakes include confusing homogeneous systems with non-homogeneous systems and mistaking non-trivial solutions for trivial ones.
Sources
- What is a trivial and a non-trivial solution in terms of linear algebra? - math.stackexchange.com
- In linear algebra, what is a 'trivial solution'? - Quora - quora.com
- 1.3 Homogeneous Equations - math.emory.edu
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