Thread: Info about coefficients of augmented matrix

In Lay is given the following problem:

Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer.





In the answers is the following:

The row reduction of to

shows that d-3c must be nonzero, since f and g are arbitrary. Otherwise for some choices of f and g the second row could correspond to an equation of the form 0=b, where b is nonzero. Thus .

This is just fine, what I don't understand however is the missing working between the initial matrix and the row reduced version. I can't even figure out which row operations to begin with.

Can someone please explain how this matix:



Row reduces to this:



ty

The second row is replaced by the sum of the second row and the product of the first row times -c.

That makes sense in such a simple way that it leaves me feeling very stupid.