Question

What is meaning by trivial and non trivial solution ?Is it like singular and non singular? closed

Comments

solving linear equations using matrix  , is not kind of sophisticated thing , there are set patterns , prefer any book , may be the one you followed during graduation. or help google.

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Homogeneous solution of equation will never have unique solution because they already have trivial and zero solution.

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Hello sandeep suri

When you say something with that level of confidence , make a habit to verifying self claim.

Why do you think zero solution(0,0,0) is not unique solution ?

Answer 1

Copying what Arjun Sir answered and adding little more

 

A trivial solution to a problem means, it is a valid solution for any problem of the same type. i.e., this solution is known to anyone and hence there is no use in explicitly mentioning it. For example, in a homogenous solution where equation equated to 0, putting all variables equal to 0 is a correct solution, but this is not a useful one and hence never really asked in any question.   

 

 

Homogeneous equation are equation which are like A.X=0   

Homogeneous solution of equation will never have unique solution because they already have trivial and zero solution.  Hence homogeneous equation can have

1) Trivial solution when rank(A) =n (n is number of unknown) and Det(A) != 0  (non singular) and

2) Infinite solution. .. when det(A) =0 (singular) they will have infinite solution.

 

 

A matrix "B" is said to be singular when Det(B) =0 ..

 

A matrix "C" is said to be non singular when Det(C) != 0