Which of the elementary column transformations, (except for interchanging the columns), will not change the solution of the system of linear equations?
I found a definiton:
Definition 2.2.1 An elementary row operation is an operation that does not change the domain of truth of the SLR represented by this matrix.
Such adjustments are:
- row replacement
- multiplying a row by a non-zero real number
- adding a linear combination of other rows to a row
- omitting a row that is a linear combination of other rows
- omitting a null row
And i want to know which of them cannot be used for column transformations to solve a system of linear equations.