Difference intrivial solution and non trivial solution in matrix
Answers
Answer:
Suppose I have system of 3 equations
a1x+b1y+c1z=0
a2x+b2y+c2z=0
a3x+b3y+c3z=0
and cofficient matrix A=⎛⎝⎜a1a2a3b1b2b3c1c2c3⎞⎠⎟ So I have been told that solution of this matrix will be non-trivial if |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=0 will satisfy given equations regardless of it's value of determinant.
Answer:
A nxn homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions.
A solution or example that is not trivial. Often, solutions or examples involving the number zero are considered trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5y = 0 has the trivial solution (0, 0).