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4utcei Uaoly ujlcnmenlatico 1R0 ColG [6"IC Inulor; Celerninalimrenu Lalllu 0 //err AtA eFte mhoknlIn eal aluve y0 Fourd eeoon * ue"mtcaatouHuneTi-col Hld...

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4utcei Uaoly ujlcnmenlatico 1R0 ColG [6"IC Inulor; Celerninalimrenu Lalllu 0 //err AtA eFte mhoknlIn eal aluve y0 Fourd eeoon * ue"mtcaatouHuneTi-col Hldc [email protected] NLMLetMecusus

4utcei Uaoly ujlcnmenlatico 1R0 ColG [6"IC Inulor; Celerninalimrenu Lalllu 0 //err AtA eFte mhoknlIn eal aluve y0 Fourd eeoon * ue"mtcaatou Hune Ti-col Hldc [email protected] nroi NLMLet Mecusus



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licre the ycllow and orangc precipirares arc, rcspectively (a) $\mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{2}, \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{-}$ (b) $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}, \mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{2}$ (c) $\mathrm{Na}_{2} \mathrm{CrO}_{4}, \mathrm{~K}_{2} \mathrm{CrO}_{4}$ (d) $\mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{2}, \mathrm{~K}_{2} \mathrm{CrO}_{4}$

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

In this problem did yet then it happened something like this. CS three CH 2 C 00 quiet In presence of Sierra two. They fast for us at media reaction will take place and product for me. CS three CS SEAL c o H on further reaction with alcoholic a witch. It will give final product ID C. H to the well born c h c cocoa page according to the option Yes. Obscenity is correct answer option B. Each correct answer for this problem.

Okay, so we're asked his objective falling. So since one is just in to we need to borrow. So we get to and this is now 11. So 11 minus two is nine. And now, since two is us and eight, we have to borrow. So this is a five, and it turns into a 12 12. Minus eight is for Okay, So now since five minus 85 is less than five minutes borrowed, we get a one here. And in the 15 year 15 a minus eight is seven. And since when is less than seven, we again need to borrow. So this has turned into four. And now we have 11.7, which is for and in four minutes for is zero and two Do not equal to okay.

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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