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: