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11,5 *9, Rotation 1 Lnergy oi xobaliar 171Seng...

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11,5 *9, Rotation 1 Lnergy oi xobaliar 171Seng

11,5 *9, Rotation 1 Lnergy oi xobaliar 1 7 1 Seng



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9. $$1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \frac{1}{9}, \dots$$

So you have that the following sequence. A one minus 1/3. One more night by this one with seven one word 81. So when I keep a general for that for the and, um with secrets so well, cervical, these want one. So what is that? Is a bit So what? We can call the zone a one. That one too. But once we no before. So as you can see one, huh? The future of these sequences old alternating because 50 17 was it the negative? Was it? Nobody wants to take things. One was the negative. So perhaps some miners one three engine builder on if you want to start at one. So we sent out one that he was my swan didn't. Why, Miss One can put another rightness there. So? So that for one is positive. And, uh, if you look at the thing in the denominator, there's not anything I do not know Terminator. So probably just something related. Also, hear the zone is three square. I'm on this. Oh, this is a mystery square that these three streak you. That's three to the fourth grade, so you can see that sequence. Well part of you have there One. When this one, the oh won over three squared one of those one Q one or before. So the whole the world would be a very strange place because the sequence can be read in us. What was that? But, uh, if you look in there like this when we have nothing so robbery onto so it's trucked. I want from you so that anyone you see people too. Um, 221 So you can have that description. Or we could give the grieve all that's on formula. You could describe Bill's away. Uh, because the relation oh, so records. He's, uh thank you. They so with some number, start with these and then we say, What is there well, for getting into the next number. Also, as you can see here as you increase the end, you're more decline by my nose. Warren Third. So my nose 1/3 time's a so Ben you just the next time, right? Because you said we'd want well to get minus 1/3. Just moved it by 1/3 to get one of her. Nine will multiply, buddy. Aw, 30 miles. 1:30 a.m. So it was You gonna come? Here's the records. Relation is, well, the previous them a hands. So bam plus one is a little A's event. Times miners 1/3. So you have those descriptions are not, Yes, so would be decreasing alternating.

To find these two matrices together. Here. First thing we need to do is check the dimensions will work. Okay? First matrix we've got is two rows three columns. That's a two by three. The second matrix is a three row one column matrix. These inner two dimensions have to match which they do. That means is a resulting matrix will be dimension the outer dimensions. Okay, So we're gonna have to buy one. Matrix is our answer just two spots here. Okay, we'll fill in the first spot. This is gonna be row one. Column one. Okay, so everything in row one thinks everything in column one negative one times six plus zero times negative four plus seven. Thanks one. Okay, this should give us negative six plus zero plus seven. That should give us a one in that first little spot right there. Okay, The second guy this is gonna be row two column one. Okay, so we're gonna take everything in row two times that same column right there. So three times six less negative five that was negative for plus two times one spent 18 plus 20 plus two should give us 40. Okay? So one in the first row, 40 in the second round, and that is the result of this modification.

We're given this magic A We're universe first. Me from the convertible meeting room. Without it, the determinant they You could have zero in a but not in veritable works. Check it. A convertible. What do you say? Actually, I read it down here. Let's find a determining a check of the convertible or not. 111 First, I'm gonna high road to buy world one by negative one and had it wrote to So I guess one might one minus one zero. Making one plus 21 No one here. Next I'm gonna multiply growth three by negative one times wrote to I get 111 negative. Q one is negative one. You know, the determining the mortification old the numbers in the pivot in the diagonal interment is clearly not so. Therefore, we can find a neighbor nullifying chambers through the over inside the right chambers on this side. Very eight in the side. You're a here you have the identity matrix for three by three One here is you here alone? Now we're gonna really do until this side here. It looks like this. Once we do that, we will get a members on this side Look for reduced. Well, we already thought before we're finding the determinant. Do it again. First they can about this here. 11 now weaken Can't hold this position here. Negative one. They won negative times. Negative. 101 Negative. 101 Here one. Now weaken. We can scale the throw here. We can divide the group by negative one. We get negative here. Also here. Positive here. Now I can scale road three by minus a few. Added row to cancel this The negative too. Times road Here. That positive you minus one. That's one. Make a few plus one minus one. Two zeros too. You get one Next. We just need get rid of this. We can. He gave the period. Rowing added to the first would be a bit of this one. Here. You never get here from zero and in one one to negative one plus 01 and 101 Now you get a second road out of the first road in negative. One plus two. Just one. You have one plus minus +10 You have minus to plus one. You hear? This is the identity matrix implies on this side. He had a members say in verse, should be one bureau minus one one, minus 12 and minus 11 minus 11

Okay, I'm reading out the formulas that we will be needing here on the top right part of our stream. So let's go ahead and get started and figure out the amount of rotation that we will be doing. So the co tangent of Tooth Ada is equal to a which is the coefficient of R X squared term minus C, which is the coefficient of R Y squared term all over B, which is the coefficient of our X Y term tell this will give us negative sex over negative six Radical three, which is one over radical three. So we know that the coat engine is one over radical. Three at 60 degrees, so to fada is equal to 60 degrees and data is 30 degrees, so our amount of rotation is 30 degrees. Let's go ahead and figure out our formulas. Actually equal Ex Prime Co. Sign of 30 degrees minus y prime sign of 30 degrees, and this is medical 3/2 Ex prime minus 1/2 wide prime. Let's do the same for why this will equal ex prime sign of 30 degrees plus why Prime Co sign of 30 degrees, which will be 1/2 ex prime plus radical 3/2. Why crying


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