Question

What is the meaning of non trivial solution math in fun?

Answer 1

Suppose I have system of 3 equations

a1x+b1y+c1z=0a1x+b1y+c1z=0

a2x+b2y+c2z=0a2x+b2y+c2z=0

a3x+b3y+c3z=0a3x+b3y+c3z=0

and cofficient matrix A=⎛⎝⎜a1a2a3b1b2b3c1c2c3⎞⎠⎟A=(a1b1c1a2b2c2a3b3c3) So I have been told that solution of this matrix will be non-trivial if |A|=0|A|=0 and trivial in any other case. As far as I know non trivial solution means solutions is not equal to zero but in any case x,y,z=0x,y,z=0 will satisfy given equations regardless of it's value of determinant.