Let's say I am doing a gaussian elimination in a matrix. When I'm turning elements to zero, I manipulate the values on the rows. could it be that a diagonal element becomes zero on one of these steps by accident?
I know I could change rows before starting the gaussian elimination to avoid pivots to be zero... but could it be a pivot becomes zero after an operation?
According to the definition, a pivot can never be zero. So I think you should use row exchange in the process of Gaussian elimination.