so we now have three equations the last equation a call from the last video sorry about that is the fact that we are going up through this last battery we're going negative to positive and so we get a positive twelve volts here equals zero at the end I no need to do the same thing with this green equation as I did with the red equation and that's the combine like terms so I'll go ahead and do that next so negative 3i to minus 6i 3 plus 12 equals 0 I'm going to be using my calculator to actually solve for these three unknown variables but before I do that I need to do some little back work with these three final equations so again my three final equations are the three of them about two star line this one here I have this one here and this one down at the bottom here and the way that I'm going to format these three equations is I want to put everything with a variable one of the I variables on the left hand side of the equal sign and everything without one of those variables on the right hand side of the equal sign and I'm just going to list those three equations all next to each other it's going to help me create the matrix that I need to plug into my calculator so the first one negative i1 minus i2 plus i3 equals zero we don't really have to do anything with that one so I'm just going to write it again down here the next equation that was that red equation that I have up here I have negative 6i 1 plus 3i 2 I don't have any I freeze I'm actually just going to leave that blank and then put an equals negative 24 and for my last equation I don't have an i1 I'm just going to kind of leave a space there I have a minus 3i 2 minus 6i 3 equals negative 12 now the matrix that I create is a matrix of the coefficients it's a three by four matrix and I ask that when you're doing these problems you write out the matrix for me so that I know what you plugged in your calculator and then you don't have to do any work other than showing me what the answer is your calculator should be so basically I'm just going down these columns the first equation has a negative 1 in front of I 1 the second equation is a negative 6 in front of the I 1 and the third equation has a 0 in front of the I 1 because there is no I 1/4 ITU's I have a negative 1 a positive 3 and a negative 3 for the I threes I have 1 0 and negative 6 and then the last column is whatever is to the right of the equal sign so 0 negative 24 and negative 12 so that is the matrix that you need okay so now we're going to plug this into our calculators and so basically I'm just going to go across and make sure that my calculator matches this so negative 1 negative 1 this is just positive 1 is the next one and zero at the end there and then I have negative six three zero and negative 24 and then zero negative three negative six negative twelve okay once you have that all plugged in you can say second quit and then you're doing some matrix math second matrix over to math keep going all the way down until you see rref it's letter b on the list hit enter and then again second matrix I put mine in matrix a so when a is highlight and I'll hit enter and then enter again if you plugged everything in correctly you should get ones across the diagonal and zeros everywhere else and then your last column should have values the first value is i1 second value is i2 third value is i3 so those are your values all you need to do is write down those values and I'm going to talk about what it means that there's a negative sign there the fact that there's a negative sign for Aitu means we chose the wrong direction when you're giving me your final answer as you list those three unfortunately I can't have these two things pulled up at the same time but as you list those three by 1 i2 and i3 you're going to give me their magnitudes and you're going to tell me the same direction as what I drew or opposite direction as what I drew okay so I have three point five one and two point five as my values so three point five amps one amp and 2.5 amps and I am fine with you just saying same direction opposite direction and same direction just make sure you have those directions clearly indicated on your diagram so that I can look at your diagram and say okay this is the correct direction this is not the correct direction so again you don't have to show me any of that work you don't have to tell me what you're doing on your calculator you just have to know what to do the things that I look for as you're doing a Kirchhoff's law problem I make sure that you have three correct equations now your equations might be different than your friends equations if you're doing them separately because you get to choose what direction you went around the loop you get to choose what your currents are and what direction they're in so your equations may not match the person sitting next to yous equations and that's fine I check them to make sure that they work with what you drew in your picture so just make sure that I can see what it is in your picture that your picture is not itty-bitty so I can't see anything okay so I look at the equations that's where you actually get half the points from if not more than half the points from because that's where the physics is the rest of it is math creating this matrix plugging the matrix into your calculator getting these final values one last comment and then we'll be done with this is that if for some reason you get a row of zeros on your calculator it happens every once in a while just pick a different equation and plug another equation in there get rid of one of your equations try something different it doesn't happen very often but it can happen so if that happens try something different with one of your loop rule equations