Question

For a non-trivial solution $|A|$ is

• A. $|A|>0$
• B. $|A|<0$
• C. $|A|=0$
• D. $|A|\ne 0$

Answer 1

The correct option is C $|A|=0$

An $n\times n$ 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. i.e. For a non-trivial solution $|A|=0$.