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I've seen a lot of times the pronoun them used like an article. For example, in the title of the Delta Rhythm Boys Them bones, or in the first sentence of "Money for nothing":     Now look at them yo-yo's, that's the way you do it.   I know that it's not "proper English" (i.e., not something you'll use in a serious writing), but I'd like to know when it's commonly used, and why. Is there any difference between using it and using the? I'm seeking for a proof of the following:     Let $A$ be an invertible matrix. Then the determinant of $A^{-1}$ equals:   $$\left|A^{-1}\right|=|A|^{-1} $$   I don't know where to begin the proof. Any suggestions? I think we need a button that says Edit and Close added to the Review Close button options.  Many of these closed posts will be around forever (and should be, closed should not just be a path to deletion), so they need editing.  If I edit it now it goes away, with the only option being a back click to get back to the review, and then click into the post and edit it.  We have an Edit and Reopen button, so this would fit in just fine. Let $f:(0,\infty) \to R$ be differentiable. Suppose that $\lim_{x\to\infty}(f(x)+f'(x))=L$. Show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$. (Hint: Write $f(x) = e^xf(x)/e^x$ and use l’Hopital’s Rule.)    My working for $\lim_{x\to\infty}f'(x)=0$:  For $\lim_{x\to\infty}f'(x) = 0$, I let $f(x) = e^xf(x)/e^x$ and applied quotient rule which then cancels off $e^{2x}$ and I'm left with $\lim_{x\to\infty}(f(x)+f'(x)-f(x))$. Can I then equate this with $\lim_{x\to\infty} \left(f(x)+f'(x)\right) - \lim_{x\to\infty}f(x)$ which then gives $L-L=0$? Is this step correct? When can we interchange “who/which" and "that”? So far I thought the words who and that are usually interchangeable:   There is the man who saw me.  There is the man that saw me.    Both sentences seem fine, who can be replaced with that. But in the following examples:   This is the man to whom I spoke.  This is the man to that I spoke.    The #2 sounds odd, which is why I don’t think it might be correct. The same observation for the words which and that, while   This is the ball which we used today.  This is the ball that we used today.    Seem to be in order and which can be replaced with that. But in the following examples the #2 sounds odd again.   This is the ball with which I scored.  This is the ball with that I scored.    I wonder if there’s any rule regarding the interchangeability of the above mentioned words. A ring of a planet has an inner radius of approximately 52,000 km (measured from the center of the planet) and a radial width of 19 km. Use differentials to estimate the area of the ring. (Round your answer to the nearest thousand.)   I hate asking questions where I have nothing to contribute but I have absolutely no Idea on how to approach this question. A step by step solution to this problem which I could apply to similar problems would be greatly appreciated, thanks in advance. Send request for "reason for down vote"? Each question in SO keeps a list of the users who voted it down. As we all know, the list is never shown to anyone. Only the down voter can see which questions he down voted.   Sometimes, down voters down vote rather hastily. Thats okay because no one is perfect (except chuck norris). But sometimes, the down voter might have a good reason to down vote but may not leave a reason behind. As a result, the poster is left wondering if his question is stupid/bad or okay. To remedy this situation, I suggest a feature below -   The poster should have a button "request down voters for reason" which can be pushed only once. The down voters in the down voter list get the notification and can choose to respond to it. I feel that this can serve as a polite reminder to those who down vote a question which would seem to be an okay (if not good) question to most people.   Example of question which I feel should have at least 0 votes -    If okay, then this feature can be combined with -    Do you agree to the proposal ?  As an aside, do you agree that the SO question above should not get negative points ? Is it possible to browse a chatroom under invisible mode? E.g.  I know that I can browse the chat when I'm not logged on. But what if I am logged on and want to spare the inconvenience of logging off/multiple browsers? How to migrate MongoDB 2.4.14 file to MongoDB 3.6? I have a database file from MongoDB 2.4 and we want use this on mongodb 3.6.  note: the file is original from the db path. Not from mongodump. This process is messy as it requires doing so on many of our clients.  Any advice will be welcomed as I'm a bit lost in this process.  Thanks Where are executables for programs stored in Ubuntu?  An application (Komodo Edit) is asking me to identify an application to be used as a web browser. I've become used to just entering the application name as a command for situations such as these, but this scenario got me thinking.   I know in Windows it would just be the relevant application folder in the 'program files' folder, but I'm assuming things are a bit different on Linux?  I thought somewhere like bin would be logical but this appears to standard Linux/Unix applications. Where would I find the binary executable for applications stored on my system? I have two exchange accounts on my iPhone 4. One that connects to my gmail, the other connects to my work's Lotus Notes. There are no overlapping contacts in the two accounts. There are also no contacts saved locally on my phone.   When I enable contacts in both accounts, I get two identical entries for each of the contacts in my gmail. If I disable the Notes exchange account, then there are no more duplicates. If I have Notes contacts enabled, and gmail contacts disabled then I have no contacts at all.  Does anyone know what is going on? Is this a problem with having multiple exchange accounts or is it a Lotus Traveler problem? (I tend to blame Notes for all the trouble in the world, but that is just my bias)  Thanks all. Let $x, y$ and $z$ be real numbers such that $x^2+ y^2+ z^2= 1$. Find the   maximum and minimum values of $2x + 3y + z$ .       How can I able to solve the problem? Thanks for your help. Error handling in C code EDIT:  The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain unanswered.  The definition of a representation is a map (a homomorphism) to the space of linear operators over a vector space. My question is: What are the corresponding vector spaces for the   $(0,0)$ Representation $(\frac{1}{2},0)$ Representation  $(0,\frac{1}{2})$ Representation $(\frac{1}{2},0) \oplus (0,\frac{1}{2}) $ Representation $(\frac{1}{2},\frac{1}{2})$ Representation infinite dimensional Representation? Getting the array length of a 2D array in Java I have two files in a directory. One has correct permissions and the other has not. Is there a way I can "copy" the set of permissions from one file to another? Find the area of largest rectangle that can be inscribed in an ellipse The actual problem reads:      Find the area of the largest rectangle that can be inscribed in the ellipse    $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.$$   I got as far as coming up with the equation for the area to be $A=4xy$ but then when trying to find the derivative I don't think I'm doing it right. I have setup a project of 250 frames with a flag and a wind force field. It works fine until I change the length of the project to 520 frames, then the flag is frozen after frame 250. There must be a simple way to change this. Thanks for any help. Regards, Daniel. When a lattice is a lattice of open sets of some topological space? When a lattice $(L,\leqslant)$ is a lattice of open (or closed) sets of some topological space $(X,\tau)$? Which conditions have to be satisfied? We may assume that $X$ is $T_1$. Using getline(cin, s) after cin