Trivial Solution Meaning

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
a1x+b1y+c1z=0
a2x+b2y+c2z=0
a3x+b3y+c3z=0

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.