Question

What does it mean the when determinant of the coefficient matrix of a system of linear equations equals zero?

Answer 1

It means that the system of equations are not linearly independent.

Explanation:

When the determinant of the coefficient matrix of a system of linear equations equals zero it means that at least one equation in the system is a scalar multiple of another equation. Hence it is not possible to find the inverse matrix and so the system cannot be solved.

An example in a 3 * 3 system could be :

`A hat x = hat b`

Where A is the matrix

1 2 3
2 4 6
7 8 9

In this case row 2 is a multiple of row 1 ( *2) and, hence the determinant is 0. Therefore `A^(-1)` cannot be found so the system cannot be solved.