Chapter 2.5, Problem 1CFU

To determine

To find: The types of matrices that are considered to be non-singular.

Answer to Problem 1CFU

The non-singular matrix has only trivial solution.

Explanation of Solution

Suppose $A$ is any square matrix.

Then we can say that $A$ is a non-singular matrix if and only if the system $Ax=0$ has only trivial solution.

In other words, we can say $x=0$ that is zero matrix is the only solution of the system $Ax=0$ .

Therefore a non-singular matrix has only trivial solution.