What does Trivial mean in mathematics?
Ans: connecting with or being the numerically least difficult case.
In maths, the modifier trivial is frequently used to allude to a case or a case that can be promptly acquired from a setting, or an item that has a straightforward construction. The thing technicality, as a rule, alludes to a basic specialized part of some verification or definition.
Trivial Solution Meaning in Linear Algebra
Let us take a system of 3 equations
and coefficient matrix “A”. So I have been told that the solution of this matrix will be non-trivial if |A|=0 and trivial in any other case. As far as I know, a nontrivial solution means solutions are not equal to zero but in any case, x,y,z=0 will satisfy given equations regardless of the value of the determinant. So, why do we call it a “non-trivial” solution?
If x=y=z=0 then trivial solution And if |A|=0 then non-trivial solution that is the determinant of the coefficients of x,y,z must be equal to zero for the existence of a non-trivial solution.
For example, the equation x+10y=0 has the trivial solution x=0,y=0. Nontrivial solutions include x=10,y=–1 and x=–2,y=0.2.
Trivial Meaning in Hindi: मामूली
We wrote trivial solutions in Mathematics higher education. But we never get into depth, sure you’d learn something today.