Why can't we multiply corresponding elements like addition is done?  Is there a specific reason why it won't be significant?   By definition, we have to multiply a row by columns.  Why such a definition other than multiplying corresponding elements?  Please ignore my ignorance. I had nowhere to ask. :(
If I multiply two numbers, say $3$ and $5$, I know it means add $3$ to itself $5$ times or add $5$ to itself $3$ times.    But If I multiply two matrices, what does it mean ?  I mean I can't think it in terms of repetitive addition.       What is the intuitive way of thinking about multiplication of matrices?
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$ (1) Does he not know? (2) Doesn't he know?  I don't usually see and hear questions formed in the first style. I was even surprised to know that it is grammatically correct. And actually it is the most &quot;proper&quot; way to form an interrogative sentence.  shows that the first style was much more popular before than now. What are your suggestions on choosing between these styles? And I will probably add the third one.  (3) He does not know?  EDIT: The answers have explained how to form a question, but have not actually provided an account on the usage of the first two forms. Especially I'm interested in the first form: does it sound formal, is it used in speech or only in writing, et cetera. Difference between "I have got" and "I have gotten" How do you determine using stat() whether a file is a symbolic link? How do I get rid of OneDrive completely? When I've worked a bit with my source code, I did my usual thing commit and then I pushed to a remote repository. But then I noticed I forgot to organize my imports in the source code. So I do the amend command to replace the previous commit:  &gt; git commit --amend   Unfortunately the commit can't be pushed back to the repository. It is rejected like this:  &gt; git push origin To //my.remote.repo.com/stuff.git/  ! [rejected]        master -&gt; master (non-fast forward) error: failed to push some refs to '//my.remote.repo.com/stuff.git/'   What should I do? (I can access the remote repository.) Explain why $E(X) = \int_0^\infty (1-F_X (t)) \, dt$ for every nonnegative random variable $X$ So if I'm correct, when you chose your starter gear and wealth you can either choose to roll some dice depending on your class and buy everything from that or you can choose the starter gear from your class and add the background items (including some gold). Here are my 2 questions:   If I choose the gear from my class, do I have to take all the equipment from only one of the (a) or (b) choices, or can I freely mix-and-match choices from the two sets? Can you spend the extra gold you get from your background on extra equipment (e.g. some soap and some fishing equipment) or do you have to start with that gold in its pouch?   The reason I ask is that I have recently created a level 1 wood elf druid and I mixed-and-matched the gear from the class, so that I chose a shortbow as a "(b) simple weapon" for the first point and a "(a) Scimitar" at the second point. My DM wasn't so happy about this, as he can't understand why I'm mixing (a) and (b).  He also wasn't so happy with me spending my 10gp from my outlander background. I decided that my druid wouldn't lay so much worth in 10gp compared to a bunch of stuff I got for that (e.g. some soap and some fishing equipment and some other useful things) and he seems to think that I'm supposed to just start with the gold instead. I have read lots of information about page caching and partial page caching in a MVC application. However, I would like to know how you would cache data.  In my scenario I will be using LINQ to Entities (entity framework). On the first call to GetNames (or whatever the method is) I want to grab the data from the database. I want to save the results in cache and on the second call to use the cached version if it exists.  Can anyone show an example of how this would work, where this should be implemented (model?) and if it would work.  I have seen this done in traditional ASP.NET apps , typically for very static data. Limit of sequence in which each term is defined by the average of preceding two terms We have a sequence of numbers $x_n$ determined by the equality   $$x_n = \frac{x_{n-1} + x_{n-2}}{2}$$  The first and zeroth term are $x_1$ and $x_0$.The following limit must be expressed in terms of $x_0$ and $x_1$ $$\lim_{n\rightarrow\infty} x_n $$  The options are:   A)$\frac{x_0 + 2x_1}{3}$ B)$\frac{2x_0 + 2x_1}{3}$  C)$\frac{2x_0 + 3x_1}{3}$ D)$\frac{2x_0 - 3x_1}{3}$  Since it was a multiple choice exam I plugged $x_0=1$ and $x_1=1$. Which means that all terms of this sequence is $1$,i.e, $$x_n=1, n\in \mathbb{N} $$  From this I concluded that option A was correct.I could not find any way to solve this one hence I resorted to this trick. What is the actual method to find the sequence's limit? Add year to question and answer dates Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $ When should I use can? When should I use could? What is right under what context? What is the standard/recommended font to use in papers? I looked around but did not find that anyone has asked this before, but what are the fonts that are standard/recommended while writing academic reports/papers? Adding CSS Reference on Site Page So I have created a Site Page that has the "New Experience" look and I would like to change its style a little. Nothing major, just the height, width, color, etc. However, I can not seem to figure it out.   For example, I tried to change the height of the .pageHeader to a smaller value.   .pageHeader{ height: 150px !important } //for example of CSS in file   Here is a reference image of the page i'm trying to change    I tried adding   &lt;link href="../SiteAssets/file.css" rel="stylesheet" type="text/css"&gt;   to the .aspx page using SharePoint Designer and it didn't work.    I also tried adding   &lt;SharePoint:CssRegistration ID="CssRegistration" Name="SiteAssets/file.css" runat="server" /&gt;   to the .aspx page and it didn't work    I tried to use the "Embed" feature to add the CSS; however, it complains and says,     This embed code doesn't seem to work. We only support iframe based embeds.   Question:   How can I add custom CSS to this type page?  I can't seem to figure it out and I'm not sure exactly why the page will not load the file.  Is this even possible? Can I Create a Dictionary of Generic Types? What are Virtual Methods? Why would you declare a method as "virtual".   What is the benefit in using virtual? The error: "mount: only root can do that" while mounting a partition I've installed Ubuntu 12.04 along with Windows 8.1. When I tried to open the C: drive in Ubuntu a window is popping out saying to run this command:  mount -t ntfs-3g -o remove_hiberfile /dev/sda2 /media/2A36EE3236EDFEA7   After running the command I'm getting the error mount: only root can do that.   What should I do? I have an application which is a relatively old. Through some minor changes, it builds nearly perfectly with Visual C++ 2008. One thing that I've noticed is that my "debug console" isn't quite working right. Basically in the past, I've use AllocConsole() to create a console for my debug output to go to. Then I would use freopen to redirect stdout to it. This worked perfectly with both C and C++ style IO.  Now, it seems that it will only work with C style IO. What is the proper way to redirect things like cout to a console allocated with AllocConsole()?  Here's the code which used to work:  if(AllocConsole()) {     freopen("CONOUT$", "wt", stdout);     SetConsoleTitle("Debug Console");     SetConsoleTextAttribute(GetStdHandle(STD_OUTPUT_HANDLE), FOREGROUND_GREEN | FOREGROUND_BLUE | FOREGROUND_RED); }   EDIT: one thing which occurred to me is that I could make a custom streambuf whose overflow method writes using C style IO and replace std::cout's default stream buffer with it. But that seems like a cop-out. Is there a proper way to do this in 2008? Or is this perhaps something that MS overlooked?  EDIT2: OK, so I've made an implementaiton of the idea I spelled out above. Basically it looks like this:  class outbuf : public std::streambuf { public:     outbuf() {         setp(0, 0);     }      virtual int_type overflow(int_type c = traits_type::eof()) {         return fputc(c, stdout) == EOF ? traits_type::eof() : c;     } };  int APIENTRY WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, LPTSTR lpCmdLine, int nCmdShow) {     // create the console     if(AllocConsole()) {         freopen("CONOUT$", "w", stdout);         SetConsoleTitle("Debug Console");         SetConsoleTextAttribute(GetStdHandle(STD_OUTPUT_HANDLE), FOREGROUND_GREEN | FOREGROUND_BLUE | FOREGROUND_RED);       }      // set std::cout to use my custom streambuf     outbuf ob;     std::streambuf *sb = std::cout.rdbuf(&amp;ob);      // do some work here      // make sure to restore the original so we don't get a crash on close!     std::cout.rdbuf(sb);     return 0; }   Anyone have a better/cleaner solution than just forcing std::cout to be a glorified fputc? Let a,b,c,d be real or complex numbers with absolute value less than $1$. Is the following true:  $$|ab-cd| \leq |a-c| +|b-d|?$$