What are the trivial and non-trivial solution of homogeneous equations in the matrices?

Kaydence Villegas

Kaydence Villegas

Open question

2022-08-19

What are the trivial and non-trivial solution of homogeneous equations in the matrices?

Answer & Explanation

blerbintiy0

blerbintiy0

Beginner2022-08-20Added 8 answers

x = y = z = 0 is trivial solution, and [A] = 0 is non-trivial solution.
The determinant of the coefficients of x,y,z must be equal to zero for the existence of non trivial solution.
For example, the trivial solution of the equation x+5y=0 is x=0,y=0. And non-trivial solutions are x=5,y=–1 and x=–2,y=0.4.
Leonidas Cook

Leonidas Cook

Beginner2022-08-21Added 1 answers

Often, solutions involving the number zero are considered trivial. Thus, nonzero solutions are considered nontrivial.

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