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Fmud 1 and (0, 01 culllch1! 2 1 Axy + 1 I: 10 0) saddlaand (0 012...

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Fmud 1 and (0, 01 culllch1! 2 1 Axy + 1 I: 10 0) saddlaand (0 012

Fmud 1 and (0, 01 culllch 1 ! 2 1 Axy + 1 I: 10 0) saddla and (0 01 2



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$\left[ \begin{array}{rrr}{1} & {2} & {-1} \\ {0} & {1} & {1} \\ {0} & {-1} & {1}\end{array}\right]$

We want to use a calculator to find the inverse of a matrix. I'm going to illustrate this with the decimals matrix calculator. So we're going to hit new matrix, identify this as a three by three matrix and then put in the elements 120 which is optional, type -1, -1 2 -10. Want us to find, then you just type Matrix A. And then the inverse. And you can then identify the inverse as 0.20 point 4.40 negative point to 1.4 negative one negative 1.2. Yeah.

Okay, so here were considered, with each being equal 0.25 on the interval of zero and one we're gonna evaluate at a 0.25 quit five 0.75 Oh, and one. Okay, But before we do that, we're gonna start by rewriting our equation that were given. So the second derivative is on its own, and that that is equal to 1/1 plus t squared times. Why? Minus one over one plus t square times. Why, prime? So make our so institutions as we've been doing where we set x one equal toe Y and X two equal to y prime, which, of course, is the same as, uh, X one prime. So that changes our system. And that will change it to x one prime being equal to x two and x two Prime be equal to 1/1 plus t squared times x one minus 1/1 plus t square times x two. Okay. And so then the initial values are I'm gonna have X one of zero, which is equal to R Y. Zero right is equal to one. Represent that his little X one, comma zero and we have our x two, the zero which is really our Why prime that were given people the negative one. Well, let that be X to come A zero. So now we can apply oilers method. And so just a reminder. Oilers method is X and plus one is equal Thio accident plus each then the function t n xn. So Step one and we have t one would be equal to t not plus h s is gonna be equal to zero plus 0.25 is equal to 0.25 right? And so, you know, we started talked about this is the very beginning as to where we were going to be, which values we would be doing our calculations on. Okay, so step two. Yeah, I suppose I should finish step one first. So that means when you take x one at 0.25 which would be approximately equal to x 11 which is equal thio x 10 plus each times x 20 So that's gonna be equal to next of one musical one. Plus, we'll have 80.25 Next to zero was negative. One eso This is 0.75 Yes, and we have that X two at 0.25 is approximately equal to x 21 which is equal to H times. Okay, one over. Mhm one plus teaser square times X some 10 minus 1/1, plus Kina square times x up to zero. Que looks pretty complicated, but we have all these values. Um and we calculated, of course, I miss one little piece here, So plus T x 20 Right, So this ends up being a 0.25 times one plus one minus one, which is equal to negative 0.5. So Step two. Here we get t two, which would be equal to t one plus 10.5. So that's 0.25 plus 0.25 is equal 2.5. So we are worried about x one and 0.5, which is a proximate to x 12 which is equal to x 11 plus h times x +21 which is equal to 0.75 plus 0.25 times negative. 0.5 that is equal to 0.6 to 5. It's mostly a lot of, um, plugging these numbers in the next two at 0.5 is gonna be roughly equal to x 22 So that is Follow the pattern next to one plus each. Times one over one plus t one squared times x 11 minus 1/1 plus t one square next to one. This simplifies to negative 0.5 plus 0.25 I'm just gonna pull this, um, fraction that we see repeating out, So I want to write it twice. Should be won over one plus 0.25 squared times 0.75 plus 0.5. According to the calculator, that is negative 0.20 six. Roughly depending on where you want Thio. Stop. I suppose a few minutes from places won't hurts. Will say 20588 Okay, we have two more of these to do. Step three. Okay, So, t three, I'm just gonna add 0.25 so it's gonna be equal toe 0.75 So we want x one at 10.75 Sequel approximately equal to x 13 which is equal to x 12 plus each x to to. Okay, so that is 0.6 to 5 plus zero point 25 times negative 0.20588 And that is 0.57353 Then the more complicated version next 2.75 is roughly equal to next to three, which is equal to x 22 plus each. Times 1.1 plus t two squared times x 12 minus 1/1 plus t squared x 22 Okay. And so we just plug these numbers and again. So this time we have a negative point to 0588 plus 0.2 5/1 plus 0.5 squared times 0.6 to 5 minus. There's gonna be plus with a minus negative. 0.20588 Okay. And the calculator says this is negative. 0.39 704 Finally, our last step here t four will be equal to one. It's 10.75 plus 0.25 So we want X one at one, which is approximately X one four is equal to x one three plus each times x 23 okay. And So that is 0.5 73 53 plus 0.25 times this negative zero point 039 704 And that is equal to 0.5 six 3604 Okay, the next two of one is approximately equal to x two four, just equal to x 23 plus h times. Let's say 1/1 plus t three squared times X one three minus x 23 I just figure out this, um, to save writing a little bit, so enjoy, right that fraction twice. But this ends up being equal to negative 0.0 39704 plus 0.2. That's a strange looking to since your 0.25 r h And then So now I'm combining this h with this fractions that B one plus 10.75 squared. And then we take the values from our previous around here, which is your 0.5 seven 353 plus zero point 039 70 four really made it. Okay. And today is a good day to love your calculator. Uh, 0.0 58 413 And so that's gonna be the last calculation. And I suppose we could have skipped that step, but we didn't. So, um, since why is equal to x one? Our approximations that we get is that why 0.25 is equal to 0.75 That why a 0.5? It is equal to zero point six 25 You have Y of 0.75 and that waas zero point 573 53 And lastly, our why of one is zero point 56 36 03

In this problem, we have given the mattresses on be an oxidant remind video. The pair of each metrics is the inverse off each other. Let's consider it Mac tricks be find metrics. Be post refined, a productive metrics A and B begin the metrics which is equals toe identity mattress. Now they find a productive be into a The result of markets would be my 00 010 three do which is not equal ist white into Demetris Since the product of too many places on either side are not I'd into demand tricks. The given to my prisons are not in rows on each other.

Industry were given jay Z is equal to zero and 1 -10 and J two is equal to 0 -10. We are asked to find human square plys. Did you to square So where to find yours happened to square? We first find german square Which is God given with love with Julian, Julian is 0, -10. We'll keep that by 0. -10. Your squares. Goodwill. No, those are the first matrix London Second Kids Don't 11 00. I understand management. Do you want to every 10100 -1000. McNabb Afghanistan zero? Management, everyone -1. That's his ego. When he saw this, you get J1 square. He's got to -100 -1. Now we will find you to square. Mhm. Which is a crypto JJ two, which is 10 -10. was declared by mm 10 -10. We will try this year one. When we get 10 -1 0. one month of a 00, that's zero. Who are -1 x 1 -100000. When you saw this we get two squares, you got to 10 minus one. Did you go? Mm No you'll find your square plus J2 square. It was a value of Germans gravity's -100 -1. Yes 1 -100. You can. So when we heard these two we get german square plus J two squared is equal to minus one plus 100000 minus one minus one minus one, Blessed Uh -1. Which is the answer this question. Mm Thank you for working with you.


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