The fundamental matrix for the system x'-B ~]x+le] [et 3e-] Which one of the following is the Wronskian of the system?Select one:a. 2b. 2e'd. e...

Which matrix is the coefficient matrix for the system?
A. $\left[\begin{array}{lll}{2} & {3} & {1} \\ {1} & {2} & {4} \\ {3} & {2} & {3}\end{array}\right] \quad$ B. $\left[\begin{array}{rrrr}{2} & {-3} & {1} & {6} \\ {1} & {2} & {-4} & {5} \\ {-3} & {-2} & {3} & {-5}\end{array}\right]$ c. $\left[\begin{array}{rrr}{2} & {-3} & {1} \\ {1} & {2} & {-4} \\ {-3} & {-2} & {3}\end{array}\right]$ D. $\left[\begin{array}{r}{6} \\ {5} \\ {-5}\end{array}\right]$

So they've given us three different Matrix sees in this problem, and they want us to described thes solutions to the Matrix. So in this very 1st 1 here we have this bottom row here that is 000 That means zero variables equals zero. This is a true statement. So because of that, we can look at the 1st 1 So that's saying an X and two y's egos equal to negative four. So because we don't know what X and we don't know why it is, we would say that this solution system is dependent. It be dependent on whatever exes or whatever. Why is to tell us what the other value would have to be in the 2nd 1? Here, we've got 106 that tells us that X is equal to six, and then we have 010 So it's telling us that why is equal to zero. That means this one has a single solution. It's not dependent X will always be six. Why will always be zero for this one toe workout? When we look at the 3rd 1 we end up with zero variables is equal to two. Now this statement we consider false, because whenever we set up these kind of equations, we always put the variables on the one side to make the equation and all of the Constance get moved over to our answer side. So if we have no variables, we should have no answer. So because we have an answer, this is a false statement, which means for this one, we can't have a solution. So any time there's a false statement included in the Matrix, that must mean there is no solution.

So were provided with this matrix here. And we're at first asked whether or not this matrix and is in row echelon form. So in order for it to be and row Athlon form the first non zero number of each row when we read from left to right has got to be a one. So when we look at this row from left, right, this is a first leading non zero which is a one from here to here also one And there isn't one here, so so far so. But the next is is that our that each one of these the next one here has got to be to the right of this. And so, yes, that is indeed the case. And then the last one is is that the last rose got to be all Not all zeros. And so this is in. So yes, it is in a roach line form. The next thing is, is it in reduced row Athlon form And this is is that every number above and below each leading non zero has got to be zero and we can quickly see that here this above is not a zero and So this is not in reduced roach Alon form. And then remember to write our system of equations here. This is the X. This is why this is a Z, and this is the number on the other side of our equal sign. So hear this. 1st 1 is X plus two. Why plus eight z is equal to zero. The 2nd 1 here is there's no acts. There's a why plus a three Z is equal to two. And then this last one is all zero, So you can leave it as is. You can always write those, uh, those numbers in in front the zeroes in front of our, um our letters here. But we do not need to do that. So this is not necessary. You can do that. And you can also write that last one at like this. So those are system of equations from this matrix here

In discussion. We are given with the questions by augmented metrics 1 to 80 0132 0000 Here we can observe that the leading element is one in 1st 1st true and all the elements below this element are zero again in next rule. Also, the leading element is one and all elements below it are zero. But in third row, all the elements are zero. Hence it is in reduced rule excellent form. In this case, we can do our equations corresponding to the Ochoa augmented metrics as X plus two y plus eight hazard equals +20 And why plus three zero equals to do that is our answer.

Hey, where are Matrix is 10 zero two zero 101 and 0013 So if I translate this back in does the equation this would be one X. There's no wise or disease equals two. This would be why equals one. And this would be easy equals. Hurry in part B, my system is the 1012 0111 0000 Therefore be no. Therefore, Z equals t z equals t. This says one. Why plus one Z equals one. So I'm gonna have why? What? T equals one? They're from a subtract one from both sides. So I have Why equals one minus T and the top equation says one x plus. He equals two So x equal two minus t and then for part C How's he is? Get on the stage. See, we have 1012 No, we have 10 zero two 0101 0003 So this bottom row here says zero X plus zero. Why plus zero Z equals three. And that's what makes it inconsistent because zero times any, there's no way to get three from from that. So that would be in consisted