For Singular matrix A: |
For Nonsingular Matrix A: |
It has no inverse, |
It has an inverse, |
Its determinant is zero |
The determinant is nonzero |
There is no unique solution |
There is a unique solution |
to the system |
to the system |
Gaussian elimination cannot avoid |
Gaussian elimination does not |
a zero on the diagonal |
encounter a zero on the diagonal |
The rank is less than |
The rank equals |
Rows are linearly dependent |
Rows are linearly independent |
Columns are linearly dependent |
Columns are linearly independent |