General Question:

Currently we are working with the Gaussian Elimination and I have some questions about the resulting matrixes.

Matrix 1: When my last row looks like in the picture, what does it tell me about the matrix and the result? What are the properties of such a matrix where I have no row with exclusively 0?

Matrix 2: What happens if I get a row filled with 0 exclusively? (Properties and result?)

Matrix 3: Can I get and transform into "odd steps" like shown there without a regular pattern? Is it allowed or not?

Matrix 4: Can my last row contain more than just one element that is not 0?

Additionally. When I transform a matrix, WHEN do I know that I can stop to actually transform? I am extremly unsure about this, because I do not know when I am actually done.

Assignment:

I need to find out the solution set for Ax = 0 and Ax = b

First of all I will try to find out Ax = b to make the first part pf the assignment easier:

So now I have some sort of steps in my matrix and i cant get rid of the -0,5. Is this okay?