trivial solution
when a system Ax = 0 has the solution x = 0
In mathematics, a trivial solution refers to a solution that is immediately obvious or requires little to no effort to obtain. Usually, a trivial solution is not very interesting or informative and it serves only to confirm what was already known.
For example, consider the equation x + 2 = 5. The solution to this equation is x = 3, which is not a trivial solution because it requires a bit of work to solve. However, if we were asked to solve the equation x + 0 = x, the solution would be x = x, which is a trivial solution because it is immediately obvious.
In more advanced contexts, such as in linear algebra or differential equations, a trivial solution refers to the solution where all the variables are equal to zero. For example, in the equation Ax = 0, where A is a matrix and x is a vector of unknowns, the trivial solution is x = 0 because it satisfies the equation. However, this solution is not very interesting since it does not provide any new information about the system being solved.
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