Trivial Vs Nontrivial Solution Linear Algebra Math

The origin of the term in mathematical language comes from the medieval trivium curriculum which distinguishes from the more difficult quadrivium curriculum. The opposite of trivial is nontrivial which is commonly used to indicate that an example or a solution is not simple or that a statement or a theorem is not easy to prove. Often solutions or examples involving the number zero are considered trivial.

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Recall that a system can have either 0 1 or infinitely many solutions.

Trivial vs nontrivial solution linear algebra math. By using gaussian elimination method balance the chemical reaction equation. In particular we may be interesting in a homogeneous linear system i e looking for. If λ 8 then rank of a and rank of a b will be equal to 3 it will have unique solution. Trivial solution the simplest solution of any equation is known as trivial solution.

C 2 h 6 o 2 h 2 o co 2. A trivial solution is a solution that can be found without even searching. Nonzero solutions or examples are considered nontrivial. Nontrivial solutions include 5 1 and 2 0 4.

For example consider a linear equation 3x 2 3. Trivial and non trivial solutions. A solution or example that is not trivial. If λ 8 then rank of a and rank of a b will be equal to 2 it will have non trivial solution.

For example the equation x 5 y 0 has the trivial solution 0 0. Thus the fact that there is at least one nontrivial solution other than the trivial solution consisting of the zero vector implies that there are infinitely many solutions. Ii a non trivial solution.