 In this video, we will provide the solution to question seven from practice exam one for math 2270 In this question, we're asked to perform the following row operations to the given matrix We are first asked to replace row one with row one minus three times row two And then subsequently we're asked to replace row one with row one plus two row three So we have to do this in basically two steps We're gonna take row one and subtract from it three times row two So taking the matrix from below we're gonna take minus 18 negative three times six We're gonna get plus six plus zero. I'm just gonna skip down one minus 24 and then plus three right here So we need to then write our matrix as we have it simple and I'm gonna do this to the to the right right here Now notice that only the first row is going to change everything else will stay the same necessarily Just copying the matrix down and so for the first row you're gonna get one minus 18, which is negative 17 You're gonna get three plus six, which is a nine You're gonna get well negative four because you add zero to it You're gonna get two minus 24 which is a negative 22 and then lastly you're gonna get zero plus three Which is a three so that takes care of the first the first operation I'm gonna slash that out because we've done it now now the next thing is we have to take We're gonna have to take row one and replace it with row one plus two times row three Whoops, so let me kind of record that down over here. We're gonna take our current row one and We're going to add to it two times row three now one thing I want to mention right here is that because of this we didn't change the second row the third row the fourth row whatsoever So in terms of the possibilities here I'm gonna be looking for a thing that have the correct second row that that six negative two Zero eight and negative one because that by itself kind of helps me out a lot Notice that matrix a does not have row two matrix B does Matrix C does matrix D does matrix E does not and matrix F does not if you look at the other ones I need to have Matrix I have to have the row row three needs to be the same so I should be zero six four two one And so which of these ones has it so C has the correct row three B does not neither does D. So honestly by what I've done already I already know that choice C is gonna be the correct one without even finishing this one I would also have to check that row four would have to be the same which it is And so then just for the sake of calculation though, let's actually complete this thing, right? If we did that we take two times row three We're gonna get a zero right here plus twelve We're gonna then get a plus eight We're gonna get a plus four and then a plus two. So notice that negative seventeen plus zero is a negative seventeen just like an option C there We're gonna get twelve plus nine, which is twenty one. We're gonna get eight minus four Which is four we're gonna get to negative twenty two plus four Which is negative eighteen and then we get three plus two which is five So this is correct if we did follow through with the arithmetic this would be correct But honestly by process of elimination we are able to figure out that choice C was the correct one anyways So either do the row operations or kind of like we did here You could use raw you could use process elimination to help you notice It's not Gaussian elimination But you use this process of elimination to help you Identify what the correct answer is that always is a true thing for multiple choice answers