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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.
This is called a trivial solution for homogeneous linear equations. (c) If the system of homogeneous linear equations possesses non-zero/nontrivial solutions, and Δ = 0, the given system has infinite solutions. We can also solve these solutions using the matrix inversion method.
Nov 8, 2016 · Trivial solution is a technical term. For example, for the homogeneous linear equation 7x + 3y − 10z = 0 7 x + 3 y − 10 z = 0 it might be a trivial affair to find/verify that (1, 1, 1) ( 1, 1, 1) is a solution.
Triviality is used to describe a result that needs very less or no effort to prove or derive it. Its synonyms are unimportance, insignificance, in-consequence, etc. Richard Feynman, Nobel Prize winner, stated- “a trivial theorem is a theorem whose proof has been obtained once”.
These solutions are called the trivial solutions. For example, consider the differential equation ′ = where = is a function whose derivative is ′. The trivial solution is the zero function = while a nontrivial solution is the exponential function
Sep 17, 2022 · A homogeneous system always has the solution \(x=0\). This is called the trivial solution. Any nonzero solution is called nontrivial.
Sep 17, 2022 · Notice that if \(n=m\) or \(n<m\), it is possible to have either a unique solution (which will be the trivial solution) or infinitely many solutions. We are not limited to homogeneous systems of equations here.
