show-that-if-x-is-in-both-w-and-wperp-then-x0

Name: show that if x is in both w and wperp then x0
Uploaded: 2017-09-21
Duration: 1 min 55 s
Channel: Numerade
Description: Show that if $x$ is in both $W$ and $W^{\perp},$ then $x=0$

Question

Show that if $x$ is in both $W$ and $W^{\perp},$ then $x=0$

Daniel Jaimes · Accepted Answer

This is problem number sixty one of this tour Capitalist states Addition Section two point three. It affects equals. This piece was function X squared. If X is irrational, zero effects is irrational. Prove that the Limited&#x27;s experts zero f is equal to zero. We&#x27;re going to approach this limit by understanding the F, as you can tell by the parts of it is a function that lines in between zero, which is its minimum and X squared, which is its maximum. So in this case, we will do our best to see if we can use eh squeezed hero to determine the limit as expert to zero for this function and with squeezed here, Um, what we do is we to recall we choose to function the one that is definitely always greater. Um around the region of exit protein A from this case zero. This function is always great enough and then the lower functions always less than half. And then we compare the limits and how they behave as limited has the element of it. Lim approaches zero for this function. Zero. That limit is equal to zero. The limit is export. Zero of this function X squared. It&#x27;s also is here instant system. It must lie between these two values. Then we have confirmed. But with the squeeze serum, the Ltd&#x27;s experts zero over their function in it must be equal to Syria.

Paul Teng · Answer

Okay, So this problem wants you to show that why goes too long? Barack satisfies the differential equation that have run over here. So we&#x27;re gonna have been atrocious. Is that we&#x27;re gonna take, uh, we&#x27;re gonna differentiate. Why was 21 over x multiple times until we get why little prime and why Prime. So when they do it only twice, and then we&#x27;re just gonna plug it in to this differential equation and see if it works. All right. So why was toe one over X that can be re written, executes a negative one? So if we were to differentiate at once, we&#x27;ll get negative accident Negative, too. If we differentiated twice, we&#x27;ll get a native one times native to which this positive two x to the negative three. So now that we have our why Why private? Why double crime? We can go ahead and plug it into these two. The differential equation. So first we have X cubed times. Why? Double crime, which equals two two x to the negative three plus x squared times. Why prime, which is people to negative X to the now you two minus x times y, which is just one of wrecks or accidents. One. All right. So simple. Finding this. Ah, the excuse. Castle level D. That&#x27;s a negative three side just to Plus, we have X squared times x a negative to those council also were less with native one. And finally, X cancels out with vaccinated Once we left with made one again and this indeed equals zero, so everything checks out.

Jack Chen · Answer

Okay, So for this program, we first need toe rear ivy or the in the following way. Tablet. You have a prime plus p eggs. Have your prime plus w we could are curious. Yuko x times w close to zero In this case, p X equals two minus one of Rex and the cure X equals two minus one, so X equals zero. It&#x27;s a singular value. We can see the other following to limit x times p x when x coast zero we have a minus one The limit x closed zero X squared times Q Eggs is zero. That means XY course zero is a regular single value with initial equation are times ar minus one minus our because it zero. This quadratic quadratic equation has two solutions. I causes your and I Costa, to which use the larger one to be the exponents. So the solution is three. Saudi has us an expansion. We denounce this expansion by Dublin two X So it&#x27;s a summation k from zero to infinity, a k extricate class, too. And we take the purity for W. And it&#x27;s a coming to do it. So we project this expansion to the left inside of the body. That gives us 11 Saudi closed to estimation K from zero to infinity que press two times K plus one. It&#x27;s up K extricate brass one miners Summation K from zero to infinity play plus two terms. A sub k extricate plus one minus submission. Clay from zero to Infinity, they said. K extreme K plus doing. We need to shift index toe. Merge all these submissions into a single one, so first we can merge it. Of the 1st 2 terms. We have submission K from zero to infinity que pass two times k times a k extra K plus one miners. Summation came from zero to infinity, a k x to the Cape houses three. So if we can see that the first time if we probably Kehoe&#x27;s there into the first time we have zero lemons. In fact, this summation should be a start. A Wave k from one. Now we can shift the index for the first term. We shift index to be K from zero to Infinity Cape Ross three K plus one. They stopped K plus one extreme K plus two For a second summation, we shift index to be K from one to infinity is a K minus. One extra K plus two. Now we can emerge off. This are both terms into one by isolating three a one x square Eso this is 11 side and we know the right hand side off this or the equals zero lamb is off. These coefficients are zero. So immediately, we have a one you causes zero and we have a recursive relation between a sub K plus one days up, K minus one. Um, so we can shift index a little bit. So we have case of two. Okay. Equals to one over to k times to keep the house too. So it took him miners. Ah, minus two. I took a pass to times his up to k minus toe. So this is the recursive relation for off the old power order order terms way only to consider be. Although that has because from this recursive relation and this is a wine causes zero. So a three depends on some constant times a one. So it&#x27;s zero. That means off these, although the terms are zero, so we don&#x27;t need to consider the order, the terms and for the evil of the terms. Um, this very case reclusive relation gives us, um, ace up to K equals 21 over. Tok process two times two. Okay, They said to K minus two, and we can keep using this recursive relation. So its upto K minus two, you closed toe 1/2. Okay, times to K minus two tons. Ace up to K minus four. So if we keep doing this Indian, we have tok pass to times two. Okay, square times to k minus to a square. Have to foursquare times two times a zero eso if we fix out two for each of which term, we have one over for three k times K plus one factorial times K factory, which is easier to right out. So our solution should be a zero times estimation cave role. Um que from zero to infinity. One over for to decay. Que pasa? One Victorio que factorial tents. A sometimes extra heat. Okay. And don&#x27;t forget, we have and exponents to here, so we need to have right out past two in the end. So this is the solution to this problem

Clarissa Noh · Answer

Hey, it&#x27;s Marissa and you right here, and we&#x27;re gonna do a proof. So since F of X is O of X, there exists constant seat and K, such such that the absolute value of F of X is smaller, equal to the absolute value sea of absolute value of X when X is bigger than king. So we&#x27;re gonna assume that Kay is bigger than one, which is a safe assumption as key as a lower boundary. Andi Chase bigger than one we can obtain. The X is bigger than one as well. So if we follow this, we got this is equal to C of C X, which is equal to see X times one which is less than C x times X, which is equal to see absolute value of X square. And by the big O notation we obtained the F of X is oh of x square with Constance Kay, um K and K bigger than one and see

Linh Vu · Answer

so we need to shut it. A ground is wrong, I think, you know, on some level ground. So no, no, I do. The definition of the F Bram on a Bonzo can beautify. Yes, the name it gets to zero. Thanks, abs. Zero. You know, I meant Thanks, man. Is there, So Doesn&#x27;t means damn it when you&#x27;ve got, you know, enemy com. Thanks. Yes, Zero. Actually, could you f accident on now? So I could just remember that. Thanks. And that would be about one. So by the problem 71 this limited to zero and similarly for the second dealing with you. You remember Lonzo got unanimity means thanks again. Zero. You know, we have and crime. I&#x27;m, uh, I What does wonders, though divine my extra Venice&#x27;s narrow. So we have, isn&#x27;t it? Thanks, Christine. You don&#x27;t have a a grand. Thanks. Confinement. Thanks on. Because I&#x27;m primed is okay. Desserts. All we have is wrong here and and from the tanks it incurred yourselves and zero

Problem

$[\mathbf{M}]$ Construct a pair $\mathbf{u}, \mat…

Problem 31 Hard Difficulty

Show that if $x$ is in both $W$ and $W^{\perp},$ then $x=0$

Answer

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David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

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