The question is about what changes the singularity, not what changes the determinant - I had checked the “Adding a nonzero fixed value to every entry of the row.”

Error message says that “it could change the determinant”, but not all changes to determinant change the singularity of the system, right?

Hello @dmokran
According to my understanding, I think changing the determinant will affect the singularity of a Matrix since the determinant of a matrix is related to its rank.

*I am having a problem typing math function in this platform but hope you will understand

Let’s walkthrough by an example:

Lets say we have a Matrix A;

3 12
2 8

The following is a singular matrix since it’s determinant is Zero: (3.8) - (12.2) = 0

So let’s now see what will change the singularity of this function:

Adding a row to another one.
Let’s add the second row to the first row, We will end up with this matrix:

5 20
2 8
det: (5.8) - (20.2) = 0

The matrix is also singular since determinant is Zero

Multiplying a row by a nonzero scalar.

lets multiply the first row of Matrix A with 10:

30 120
2 8
det: (30.8) - (120.2) = 0
The matrix is also singular since determinant is Zero

Switching rows.

Let us switch the two row of Matrix A:
2 8
3 12
det: (2.12) - (8.3) = 0
The matrix is also singular since determinant is Zero

Adding a nonzero fixed value to every entry of the row.

Now let us add 4 to every row of Matrix A:
7 16
6 12
det: (7.12) - (16.6) = -12

As we have seen “Adding a nonzero fixed value to every entry of the row” has changed Matrix A from being a singular matrix to a non-singular matrix.

I am yet to watch the previous videos of the course so there might be some other approaches to your question.