I am in a calculus class where we are learning the introduction to row reduction. I have done this before in other courses, so I am familiar with the process, but I am not sure about this one. We were given:
x4 + 2x5- x6 = 2
x1 + 2x2 + x5 -x6 = 0
x1 + 2x2 + 2x3 - x5 + x6 = 2
We were supposed to: solve for each unknown or tell how many solutions this has(usually something like 0 or infinity).
The Attempt at a Solution
We haven't learned it exactly yet, but there is no real row eschelon form for this, is there? I don't know what all I can do mathematically, it just seems to me that we only have 3 equations and 6 unknowns, so we cannot possibly solve for this, right? Am I missing something here? I wrote out the matrix exactly as it is written (if it didn't state a variable, i set it to 0. e.g. in equation 1, it does not mention x1 through x3 so I made those 0).
No matter what you do, you have a 3x6 matrix with 3 equations and 6 unknowns.
Am I missing something here? How could I mathematically answer this question and not just state what I have stated above?
Any help would be appreciated, thanks.