4

Lecf(c) = (22? + 2)8(-52? + 2)14(e}...

Question

Lecf(c) = (22? + 2)8(-52? + 2)14(e}

Lec f(c) = (22? + 2)8(-52? + 2)14 (e}



Answers

$E=2$

So for this problem, we have the information. A sub one is equal to one over e in. Our common difference is to overeat when we can get this information by looking at our Siri's, so rewards plug into the formula. A sub n is equal to a sub one plus and minus one times d. So we have here 21 over e is equal to one over e plus to overeat Times end minus two overeat. So I'm just plugging in all of our values and distributing the d here. So when we simplify here, we'll get 21 over e is equal to one minus one over E plus 2/3 times in. So now we can simplify this even further. We will get 20 to overeat is equal to to overeat times in So our east cancel out and we're left with here 22 divided by two gives us 11 which is n and here is equal to 11 For the next portion of this problem to actually find the some we're going to plug into the equation. Here s sub n is equal to an over to times a sub one plus a seven. So we have here that's up. 11 is equal to 11 over to times one over E plus 21 ovary. So again, I'm just plugging her values in. So when we simplify here, we'll get 11 over to times 22 over e and that will give us here. So if we cancel out 22 as the 22 divided by two gives us 11 11 times 11 gives US 121 over E, which is our final answer.

Ah, good day. This is question number 22 and we're looking at the vectors accent. She and Wyatt t here. And in this case, I didn't really bother writing down the whole problem. You can read it off, but basically, there's a few stuff to this. And the 1st 1 is to look at whether or not exit e and y of tea. Barb, a fundamental solution said for the homogeneous, homogeneous linear equation, X prime equals t a X. Um Okay. So, again, I don't you They used a notation x one x too, but I just used excellent. Why? Which is a big deal, I guess. But still, um Okay, So since exit t and y of tr to actors meaning they're two dimensional or to have two coordinates, it is enough to check the ron skin. And in this case, um, so the wrong skin is just the determinant of this matrix. And, um, you know, if you do the algebra again, this is a two by two matrix you should buy. No. Now know how to calculate the determinant of this? Ah, you end up with negative Clyde E to the three t and that you can check that w zero is not zero. It's in fact, equal to negative five, meaning that Exit E and Y a T form of fundamental solution said Okay, so the first answer is yes, they do form. Ah, fundamental solution. Set. Um, and the accept being the fundamental matrix is exactly this guy here. This is your fundamental matrix. The definition off the, um, Ron ski and, uh comes from the fundamental matrix. Okay, so the final question is toe thio. Find the general form of solutions. And to that end, this here, uh, Z f t is a general solution, general form of solutions. And, um Well, I just, um you know, if you if you wish, you can write the, uh like this, but I wouldn't it this is just simplifying or I don't know. You even know if it's simplifying, but actually computing. Um, this z of two I don't really think of it is simplifying anything, but that's what it is. So Okay, so that's your general form of solutions. So, um, just, uh that's the answer to your question. Uh, thank you.

2.2 plus negative 2.2 plus 2.2 We have some opposites here, so let's go ahead and use the inverse property first. If we add 2.2 plus its opposite negative 2.2, we get zero. Now we have zero plus 2.2, which is the identity property. If we add zero to any number, the result is that number the full some 2.2 plus negative 2.2 plus 2.2 is equal to 2.2.


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