5

Tho comect siructure 0l methyl-A-D-altrofuranoside I8;ChOHo=OkOHOhCrohaltneHOHO_OHOCH;HQHQHO HO OHHO(D1OCH;OCH;OHHOHOOh HoOHOCH,...

Question

Tho comect siructure 0l methyl-A-D-altrofuranoside I8;ChOHo=OkOHOhCrohaltneHOHO_OHOCH;HQHQHO HO OHHO(D1OCH;OCH;OHHOHOOh HoOHOCH,

Tho comect siructure 0l methyl-A-D-altrofuranoside I8; ChO Ho= Ok OH Oh Croh altne HO HO_ OH OCH; HQ HQ HO HO OH HO (D1 OCH; OCH; OH HO HO Oh Ho OH OCH,



Answers

Whar is the corrcct ordcr of rhe srrength of hyclrogcn bonsls? (a) $\mathrm{NH}-\mathrm{N}<\mathrm{OH}--\mathrm{O}<\mathrm{TH}-\mathrm{F}$ (b) $\mathrm{ClH}-\mathrm{C}_{1}>\mathrm{NH}-\mathrm{N}>\mathrm{OH}-\mathrm{O}$ (c) $\mathrm{ClH}-\mathrm{Cl}<\mathrm{NH}-\mathrm{N}<\mathrm{OH}-\cdots \mathrm{O}$ (d) $\mathrm{NH}-\mathrm{N}>\mathrm{OH}-\mathrm{O}>\mathrm{TH}-\mathrm{F}$

In this video, we're gonna go through the answer to question number 19 from chapter 9.3 to rush to find the inverse matrix off F S R E O X, which is a matrix as a function of time given here. First, let's recall that inverse off a product major sees a B is equal to the inverse off B plans by the invested a sharing all of the investors exists. So let's think about how we can write this in a slightly different way. So we kind of want toe, not have to worry about all the u to the t You need to mine it easy to tease. So let's just write the coefficients first 14 and then you see that all the first row almost quite by eating Timmy on the second row E to the minus t you know, 30 points to t so we can turns up by e to the t zeroes ever in the second row zero e to the minus t zero and 3rd 1 00 each of the two teams. Okay, let's call this one a on. Let's call, this one will be, Then we can use this formula to find the total invest. Okay, so first up, let's find inverse off, eh? Let's do it in the usual reduction way. So what we got 111 one minus one. See? You want one? Combine that with the identity. 100010 There. Is there a woman? Okay, we're reducing. Let's subtract the first row from the bottom room. That gives us 00 three minus 101 less. Attract the first road from the second road zero minus 21 Uh, then screw reminds 110 leave in the first row is it is one warning zeros era. Okay, so try it times in the bottom row by 1/3. We got 001 minus 1/3 zero 1/3. Get me. Okay, then this new bomb row, we can subtract that from the 1st 2nd most. So from the first room gonna be 10 because I want one. That one minus one is zero. It's gonna be one minus a bird. Sorry. One minus minus. A bird, which is one plus a bird, which is 4/3 zero minus 00 zero minus 1/3 as much bird. Then subtract the new bottom row from the middle road is your, uh, minus two zero minus one minus minus 30 miles. Off course, a bird which is minus two birds one minus zero is just 10 minus. The third is my herd. Okay, so bottom row stays the same. 001 Mines third, zero third. Let's multiply the middle Robot minds heart to get 010 Ah, my hard times minus 2/3 is 1/3 then one times minus half is mine minus half minus. 1/3 is 16 Then let's do the top road minus this new middle road. Then we're gonna get the matrix on at the identity matrix on the left for the 4/3 minus. Good. This one zero minus 1/2. It's okay. Zero minus minus 1/2. It's 1/2 on minus. 1/3 minus suit is minus 36 Which is my heart. Okay, so this is our inverse off the function called a Now it's fine. In burst off. I actually called bay. So be waas. Eat the tea. 00 zero. It's the minus t zero. Is there? Uh, zero. He said to take the inverse of this. This is really easy. Um, because when you got a non zero elements in the leading diagonal on and it's just the reciprocal off those beating darknet values on the rest is all zero. So eat the minus t 000 e to the T they were zero zero. Eat some honesty. Sorry. He's the mind to t expended in verse off X, which is inverse off. Maybe. Which is? They invest a inverse, which is, if the modesty 00 zero e to the T 000 into my studio tea. That's our invested. Be invested a waas one, huh? Minus off that, But it's hot. Six minds of the zero Third. Then when we we'll find them together, it's question, but we got E to the minus. See, huh? Modesty minus ah, the money's team. Bird eats the tea. Mine's 1/2. It's the mind. Yeah, it's the team. Six. It's the team, but Murray get minus. 1/3 eats the minus Tootie zero on the third eats the mind stated, and that's I invest

But today we're looking at question number 18 in the textbook, which asked whether the three vectors except T Y o T and Z f t are literally independent or liberally deepened. Okay, First comment I should have to make is that I cannot use the Ron skin here. Why? Because the Matrix here, the matrix X city is not square. So this is not a square matrix. So the Ron ski and method is out, and that means that I must use linear the definition of linear independence. But I think this question is actually a nice, um, a nice question to better understand the concept of linear independence here because, uh, it's is I I think it is. You'll see in the end that I think I think it's a nice question. So assume that there exist number Xavi, and see such that, um, for every ci, I have, um, 18 holding. So for every t 18 holds Okay, Uh, then in particular, I know that this 18 holes for both are equal zero and as equals pi over too. Okay. And now, if I evaluate 18 at our equal zero, I see this. I get this expression awesome. I'm really just plugging in here are equal zero into each of the, um of the vectors. Yeah. Yeah. Okay. And, um And then, uh, when I do that, I get I end up with a equals A will see equals zero, and that's just solving. That's just solving the system of, um, that's just solving the system of linear equations. Okay, So, evaluating our equal zero, I get a cool sequel zero and then evaluating a pie over to ay, enough with something very similar. And now again, I'm just evaluating 18 of just plugging and pie over to it in, um, in all the vectors in 18. And when I end up again with ankles, be equal zero. So this means then that if 18 holes for all she I must have, uh, a equals B Equal sequel zero. It's the only values that hole that could possibly work. Remember, A, B and C are fixed numbers here so they don't bury for T. They're just fixed. And that's exactly what it means to be linearly independent. So So that tells us that Excellent Wa x, y and z earlier Really independent. And I think this is a nice ah, a nice example off the definitions

Okay, so we have here. Don't be scared. Erase of the negative p minus de la school. Sign or be and you want to find its LaPlace transform. So to solve these, we can express this ass the blast transform off duty squared my no absurdity a raise in the negative. T mine us the restaurant's form off the class. The restaurants form off. Go sign or be This is just equal. Do to LaPlace transform off the square is the negative p So we just transferred to on the outside apprentices, my nose, The blessed transform off he plus the plus transform off. Go sign for peak. So you think the plasterers foreign table We know that the LaPlace transform off p squared. Erasing the negative p is just equal toe to for Auriol all over as this one Kyul, the LaPlace transform off being is just equal. One over s word and the LaPlace transform off. Go sign 40 is just equal. Toe s over. Eskridge last 16. So, Saul, being for this, we know that no factorial is just tickle toe. So we have to over express one You So did I think the whole equation We know have f s as a 12 toto times over. S press one cube minus one over s squared. Plus as over Escorted 16. So the further simplified these our fine an answer would be for over s plus one cube minus one over Eskridge, plus as over as squared. Plus 16. So this is our final answer. So if you're if you can notice one of the most important thing when doing when doing the last transform is for you to be to familiarize Recep, it'll oppressed, transform people. So from there, we can get all our answers. I'm sorry by knowing the values off now. Not blessed. Transform. So this is our final answer. So F and C is equal to four over s plus one cube. Um s press one race, two Q minus one over X squared plus s over s scripless Expedia.

So in this problem we're given this matrix which Is a diagonal, right, only has entries on the main diagonal. Everything else is zero and were asked to define the determinant. We can use a matrix calculator to do this with. So what you desmond dot com went to math tools matrix calculator and got this one. So I need a new matrix now and I got five rows and five columns. And the first entry up here Is a -2 And then the entry here is a three And the entry here is a -1 man. She just working my way down the main diagonal here, This is a two And the last entry down here is a -4. There's all my entries now to do the determinant. I go d E t of a and We get -48 for the answer. So there you go. Which by the way, if you multiply the entries on the diagonal there. Look what happens When one is 2 times three is -6. I was in -1 is plus six times two is 12 Times of -4 is -48. Gave us the determinant, didn't it?


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