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Question

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Answers

$$ \left[\begin{array}{llll} 0.01 & 0.32 & 0 & 0.04 \\ -0.01 & 0 & 0 & 0.34 \\ 0 & 0.32 & -0.23 & 0.23 \\ 0.01 & 0.96 & -0.23 & 0.65 \end{array}\right] $$

So given this coding scheme we have over here, we want to decipher these four words. So let's go ahead and start with a capital A. So we would start from the left, so it's gonna be zero. So we don't have anything for that. That it 01 still don't have any thing for that? Then we have 011011 that's going to be represented by T. All right, then we move on to 11 is represented by E. Then. So we already said that 01 wasn't anything. So we can look at 010 So I don't say anything there. But then we have 01 00 and this is s. And then we have 011 which again we already said that was t so a is a coating for the word test. Right? So now let's move on to be here So we don't have anything for zero or double zero or three zeros. But we do have something for a 0001 And so this is the letter be ah, one we already said was the ease that's gonna be and then we have one again. So that's another E. And then lastly, we're going to have so 0000 So that's are all right. Now, let's move on to see, All right. So again, we don't have anything for zero or 01 Um, 010 Nothing. But we do have something for a 0100 And this is s all right, then. One again is hey, and then so 01 We don't have anything. 010 Nothing. Zero ones there. One Nothing. But we do have 01010 in. This is X. So see is a coding for sex. Then for de So again we would dio so zeros Nothing. 01 Nothing's there. 111011 is t thin. You could see that zero zero's one is a And then again, we already said that. 010101 Well, this is X. So D is a coating for the word tax.

In this question, we have to use technology to find the inverse of the given metrics. There is our metrics. No, we will use matrix algebra tool in order to find the inverse of these metrics. So here is a tool. This is our tool. Now we will enter the given metrics. A hell. We have entered the Cuban metrics. Now we will and the formula Hair, which is in bus. Now we will enter on compute and this is a inverse metrics. So invest matrixes, right 91.35 -8.65 zero -71.3 -0.07 -0.07, Deal 2.49 2.6 2.6 -4.35 1.37 2.69 2.69 zero -2.1. Thank you.

So they want Severo, if these coatings for these letters here is a prefix code or not. So one way we can go about doing that is create a binary tree and then see if there's really any branching off the letters. Because if there's no brunch, I get all that is really easy to say that it will be a prefix co. So let's go ahead and see if we can do that. All right, so for a So it says we're gonna go 11 So we just have a branch where it could be zero or one like this and then off on the side of be one again. So okay, that's gonna be where we place a now for E. It says would go zero and then we'd go zero again. So we have either Then for tea. It's as we go one and then zero says can go toe looked sweet, place t there and then for s it's zero and then one so we can place s there. And so now notice here that all of these were really just at the ends. These are all just leave. So because of that, we can go ahead and say that this is prefix code. So let's do be now. So first it says we're going to have zero and that's going to be a And then if we choose E is going to be just to kowtow one and then t is 01 So it goes zero and then one. And so now notice how we have this branching right here off of a Well, that means if we were to write 01 well, we could actually have where this means two different things. It could either mean a E or it could just be t. So because of that, this is not going to be a prefix coat. So let's try the same thing with C. Okay, so we have zero or 101 says, go ahead and put that down first. So we go one zero and then one, and that's going to be a then we're going to go 11 so we would branch off this one and put eat there. Mountie is going to be zero zero one s is going to be zero one one. So that's s and that in is going to be 01 zero and that's it. So no news here that all of these are also just leaves. And so because of that, we have no ambiguity. If we were to try to create anything, so this would be prefix code and then for our last set, let's go ahead and just scoot all this down really quickly. So we'll go ahead and see if we can create a nice little tree from this. Right? So a is. So we start with zero and then one and then zero. And so this should be a then for E. This is going to be one one. So you have V out there, then t is going to be 01 one s is going to be one. So zero, then we have one one, and then I is going to be one zero one zero one and then I is down here and so again, you can see all of these just end up being leaves. And there is nothing where we might have some ambiguity as having one letter here or not. And so because of that, we can also say that this for D will be prefix

They want us to control binary trees or these prefix codes that they give us. All right, so let's go ahead and start with a here. All right? So we have a so four to code the letter A is going to be 11 So So we're gonna start from appear and we're gonna zero one. And then here we could go to zero or one, but we just want to go towards one. So let's do that. So we're gonna place eight out there now for E. So that's just zero. So we just have e here, then for tea, that's going to be one. And then we need to go zero and then one again. We're gonna go to the right place to be there and then, lastly, for us. So it's 10 Look it left and then again, zero. Then we place s down there. So this here would be the buying cherry tree for our coding scheme for a and you can see it is a binary or a prefix coding, because we really don't have any ambiguity since all of these are just leaps. Okay? No, let's go ahead and do be so it says we're going to start with a being just one. So we started here. We drove to the right one. And then that's gonna be a, uh then for E. That's going to be 01 That means we need start toe left to go there for zero. And then we'd go to the rate for one answer than we place E here. So for T, it says we're going to go zero and then one. And so then we place t right there and then s So we need to do 03 times will go left three times that one too. Three. And then we go to the right once and then that's going to be s. And then lastly for and we're gonna do 1234 left. So 123 four and then we go to the rate for one, and then that would be in. And then you can see that all of these air going to believe so makes sense that this is a prefix coding. I got a little bit better for my box and then for our last one over here. Okay, so it says a we need to go to the right because of one. And then we need to go to the left for zero. And then we would go to the right again for one, and then we would go to the left again for zero. And so that's going to be a now he is just zero. So that means we just go to the love you put zero there and then we place E down there and then t well, that means we go to the right twice. We go one and then want to get and then for s, we're gonna have one. So we go to the rate zero, go to the left, and then we go to the right for one, and then we go to the right one more time. So that would be yes. And then for in is gonna be one zero. And then we need to go to the left again for zero and then to the rate for it. And then lastly for I So we go to the right once they were going to go left three times so one too, so that we need to put an extra branch here and then we go to the rate one time, and then that's going to be I. Then again, you can see that all of these are just leaves, so we really don't have any ambiguity for any of us, and so this would be are buying territory for that coating?


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