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What is a trivial solution of a homogeneous system?
What is a trivial solution?
When a system has a nontrivial solution?
Is a solution that does not consist of all zeros trivial?
Since the zero solution is the "obvious" solution, hence it is called a trivial solution. Any solution which has at least one component non-zero (thereby making it a non-obvious solution) is termed as a "non-trivial" solution. – Anurag A. Aug 13, 2015 at 17:26.
- What is a trivial and a non-trivial solution in terms of ...
A solution which does not consist of all zeros is not...
- What is a trivial and a non-trivial solution in terms of ...
Nov 8, 2016 · A solution which does not consist of all zeros is not trivial. The trivial solution means that all the variables are zero (i.e. the solution is the zero vector). If the system is homogeneous and it has a unique solution, it will always be the zero solution.
A vector formed by all zeros (zero vector) is always a solution of any homogeneous linear system and it is called a trivial solution. Any other solution than the trivial solution (if any) is called a nontrivial solution.
Any solution in which at least one variable has a nonzero value is called a nontrivial solution. Our chief goal in this section is to give a useful condition for a homogeneous system to have nontrivial solutions.
Sep 13, 2020 · A trivial solution is a solution that is obvious and easy to find. A non-trivial solution, on the other hand, is a solution that is not so easy to find. How to find an unknown...
- 13 min
- 113.1K
- Ganesh Institute
Sep 17, 2022 · We call this the trivial solution. If the system has a solution in which not all of the \(x_1, \cdots, x_n\) are equal to zero, then we call this solution nontrivial . The trivial solution does not tell us much about the system, as it says that \(0=0\) !
Sep 29, 2021 · This video introduces homogeneous systems of equations. Then it explains how to determine nontrivial solutions.
- 9 min
- 7.5K
- Mathispower4u
