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(10 points) Let A =[:4 Find the pivot positions Ad pivot colus of -1...

Question

(10 points) Let A =[:4 Find the pivot positions Ad pivot colus of -1

(10 points) Let A = [: 4 Find the pivot positions Ad pivot colus of -1



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In Exercises $1-4,$ find the coordinate increments from $A$ to $B$.
$$A(1,2), \quad B(-1,-1)$$

Uh this isn't common to talk about increments. Uh and a lot of math classes, but from the context clues. Uh It sounds like it's very similar to the idea of slope because slope is defined as change and why over change in X. You're probably familiar with that. Um You may be familiar with rise over run or you know, y tu minus Y one over X two minus X one. Which is exactly what we'll be doing in this problem. So maybe I'll do this, I'll just kind of that's what I'm going to be doing. So when we're given that point A Or -32 and point B. Was negative one uh negative too. Um And I'm going to go from A to B. So my change and why I'm gonna represent it as the B. Is my Y to value. So maybe I'll even write it down Y two. And then over here this will be X. Two. And then up here would be X one. And right here would be why one. So my change and y will be a negative two minus two. I hope you see where I'm doing the substitution there. Uh to give me -4. So the increment the change and why is a value of -4. And so doing the same thing with my change in X. I'm doing X two minus X one. So I labeled X two as negative one. And when I subtract off negative three, Uh that's really the same thing as 91-plus 3. I don't know if you need to see that word, but you're changing X would be positive too. Um Again, this is not really a term that's used often. Uh in calculus we talked about slope a lot more changing my over change in X. But the context says it's the same thing.

In this exercise, we want to find the coordinate increments from eight a beat so we can think of it like we have a point. A in a point B. Of course, these are not gonna be drawn to scale of what once actually are just a visual representation for us to get an idea, we have A and B So if we're trying to find the cornet increments, we're looking for the change in X and the change in why? From a to B school right here, changing X equals and change in y equals. So the change in X from a we have X equals zero and then a B, we have X equals zero. So there's no change in X zero. We're moving zero. But for why a we have why equals four and B we have why equals negative, too. So to get from four to negative to, we have to decrease by six. We could just take four and subtract negative to four minutes of four minus negative. Two is six and that is our coordinate in quince

Okay, So here is our giving matrix. Now the minor of, um, the element in the first row. First column. That would be, um, sub 13 That's gonna be equal to we eliminate the first role in first columns with at the results of matrix, we have 003 41 14 for 12 Okay. And then take the determinant of this matrix. So here we have zero minus zero plus three times. Uh, four times one minus four times one, which is equal to three times four minus four, which is equal to three times zero, which is equal to zero. So therefore Mm. So 13 matter here is equal to zero, and then the cool factor of the entry, um, it's gonna be see someone three. That's just equal to negative one to the one plus three times the corresponding minor. Okay, but the manner is zero native one. Okay, forced one time, zero. But anything Times zero is equal to zero. So forced The cool factor here is gonna be equal to zero. Okay. And then looking at part B, we're out the minor of the entry in the second World Second column we get by eliminating the second roads in column. So there will be m sub 23 is equal to four. Negative. 16 41 14 412 Okay, let me take the determinant here. So we get while we get four times. One times two minus 14 times. Once we get four times two minus 14 plus one times eight minus 56. Plus six times four minus four. This is our four times made 12 plus one times made of 48 plus well, plus zero plus six times zero always is plus zero. So we get negative. 48 um, minus 48 because zero, which is negative 96. So therefore the minor here, except to three, is equal to negative 96 in the cold factor of the entry in the second one second column. Let's see, some 23 gonna be equal to negative one to the two plus three times the corresponding minor. So negative one power. So we just get native 96 times the native one, which is equal to 96. Okay. And then, um, per seat the minor of the entry in the second row. Second column That's M 72. That's equal to the determinants. We get crossed out the second row. Second column looking at the corresponding matrix we have 41640 14 432 Okay. And then take the determinant here. Um, so we get four times while zero minus 42. That's four times negative. 42 um, minus one times eight minus 36 of minus one times and negative. 48 plus six times 12 minutes. Zero plus six times 12. Um, which is equal to negative 1 68 plus 48 plus 72 which is equal to Ah, negative 48. So therefore minor here have a substitute is equal to negative 48. The cool factor off the entry. Uh, that would be C sub tutu. Okay. Native oneto, a non power times. The minor is just one time is a minor is the cool factor here is equal to negative 48. Um, And then, uh, party. So the minor of the entry in the second row first column, um, started b m up to one is equal to determined to get by crossing out the second rolling first college. So we get negative. 116 10 14. 132 Kids, take the determinant here. Um, and what we get, uh, well matter space. Um who? All right, let's come up here a little bit. I guess I'm come up with is the race. Thats part. Have space. Let's just race here, E I think we're almost done Science. Give ourselves a little extra room. All right. Um Hmm. Okay. So, um all right, we have minor. Which from taking the determinant of the matrix. Um, So what we get is well, we get negative. Um, needed one times the chairman it here. Zero 14 32 then minus took. Minus one times determinant. 1, 14 12 And then plus six times the determinant out. +1013 So we get, um, native one time zero minus 42. That's 42 then minus one times two minus 14 Which becomes, um, minus one times, minus 12. Plus 12. And then plus, um, six times, two minutes. Zero. So this plus six times three, which is a plus 18. So therefore we get that ends up to one. Ah, minor here is equal to 72. Okay, and then, lastly, just looking to find the cool factor started. Bc sub 21 Well, it's gonna be on opposite side because two plus one is an odd the most negative 12 An odd power is negative. One time 72 is equal to negative 72.

Hello. So here we have the some we have I going from 1 to 10 of I minus one times four I plus three. So we can do we can split this up as well. This some um going from I to 100 of while we did if we to foil this out this or distribute we get a four I Squared -I -3. So this is going to be equal to again to some where we have I going from 1 to 10 of Well this then becomes a four, I squared minus I minus three. Which we can then break up as the individual terms. Here is we have the sum of while four I square the four can come out front of the some nation that's going to be equal to four times the sum I going from 1 to 10 of I squared. And then we have minus two some where we have I going from 1 to 10 of just I. And then we have minus to some uh where we have I Going from 1 to 10 of just three. So therefore well this first um I square we know the formula for um the some I from one to end of I of I squared. So that's going to be we have the four out front and then that's going to give us um for Times 10 times 10 plus one times uh two times 10 plus one. And then all divided by six is our formula for the some of the first and squares and then we have minus or the sum I close 1 to 10 of just I that's going to be well 10 times 10 plus 1/2. Yeah. And then um minus well um the some I was 1 to 10 of just three. That's just three plus three plus three plus three. There's no eyes in the last some here, that's going to be equal to about 10 times so minus three times 10. Yeah. Okay. And then it's a certification here. Um we certify this, this becomes uh for this whole part here just becomes um Uh 385 so we have four times 385 and then we have minus while this here 10 times 11/2, that's 55. So we have four times 385 minus 55 then minus three times 10, so minus 30 and that should give us 1455. So the sum here is 1455. Mhm. Mhm.


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