How to find the eigenvalues of the following tridiagonal matrix
Calculating the eigenvalues of a matrix
For usability reasons, for example in , the 'viewed' counter should show as  ...instead of... . It's much harder to decipher that there are a million views on the question just by looking at it.  Some people in the comments pointed out internationalization concerns with it. I do think that since there might be a problem with it, that spaces would probably be a better idea. By default, all browser instances use the same cookie for the same site. Is there a browser that doesn't follow this?  Or is there a Firefox plugin that can "wear" different cookies for a specific site? Xcode 6.1 won't let me create a new project I'm running Xcode 6.1 on OS X Yosemite and I'm unable to create a new project, as you can see below it just says 'loading'.  I've removed the product and org name for the purpose of this image. I have tried uninstalling but that didn't work. I am new to Xcode and coding in general so I would appreciate it if any solution could be given in lay terms. I'd like to ask for help with a task that I've been given.  The task goes like this: In a poker game (52 cards), 5 players are given 5 cards each. What is the probability that both the first and the third player will get a full-house?  It's apparent that the probability of the first player getting a full house is  $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}}$  Then the second player gets 5 random cards, so $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5}$  Now the third player is supposed to get a full house, I'm assuming it should look like this: $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5} * \frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{42}{5}}$  The fourth and the fifth player both receive 5 random cards, so the final equation should be:$\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5} * \frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{42}{5}} * \binom{37}{5}* \binom{32}{5}$  This is how I would solve the task, but I'm not sure that my solution for the third player is correct. Could anyone more experienced than me have a look at my solution?  Also I'm sorry if there is a solution for this type of task on this site, I tried looking for it and I found a lot of poker probability questions, most of them were however focused on only one player and not multiple players, which is my case. Badges loading broken in election statistics We have an  and I noticed the badges are not loading in the election statistics like they should be. It just hangs forever loading badge information:    Unfortunately I blew off reporting this for a couple days figuring it would resolve itself, but it doesn't seem to be a temporary problem. prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit Convert short[] into a grayscale image Removing minimize/maximize buttons in Tkinter Prove that in any GCD domain every irreducible element is prime Hint:  $a^2 -ab +b^2 = (a+b)^2 -3ab.$  I know we can say that there exists an $x,y$ such that $ax + by = 1$.  So in this case, $(a+b)x + ((a+b)^2 -3ab)y =1.$  I thought setting $x = (a+b)$ and $y = -1$ would help but that gives me $3ab =1.$  Any suggestions? Fingerprint activation in Dell Vostro 14 in Ubuntu 18.04 I have Dell Vostro 14 with OS Ubuntu 18.04.  I tried   sudo apt install -y fprintd libpam-fprintd   but not able to use fingerprint reader of my laptop. Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog For all $n \in \mathbb{N}$, $n &gt; 1$ and $x,y \in \mathbb{Z}$ prove that      \begin{equation}   (x+y) \text{ mod } n   = ((x \text{ mod } n)+(y \text{ mod } n))\text{ mod } n. \end{equation}   Would this be a proof if I say:  Let $x = x' \text{ mod } n$ and let $y=y' \text{ mod } n$. Then  \begin{equation}   x+y = x'+y' \text{ mod } n. \end{equation}  Now, if we look at the current thing we want prove, this will follow:  \begin{equation}   x+y \text { mod } n = (x \text{ mod } n + y \text{ mod } n) \text{ mod } n. \end{equation}    I'm not sure if this is allowed or will count as a "proof" at all. Maybe you can show me some other ways of doing this, more precise ones? What if client doesn't like any logo design concept? I'm in a process of creating Graphic Design contract. I've decided to provide each client with 3 logo concepts and 3 rounds of revision. Ideally, I would create 3 concepts and client will chose one, but it happend to me before that client didn't like and concept and I end up with doing 10+ more (yes, I've worked without contract).  How can I prevent this situation? Should I charge hourly for each new concept separately? How can I express my thoughts clearly in a contract (without sounding like 'if you don't like any, you'd have to pay more)? I don't want to scare client and put thoughts into their minds saying that there is a possibility that they won't like me ideas. In the United States, we say that someone lives on a street, whereas I've noticed that British people say in. For instance:     Bubba lives on Washington Street.   Colin lives in Cavendish Avenue.   I believe we both would use at when a number is given. For instance:     Bubba lives at 16 Washington Street.   Colin lives at 7 Cavendish Avenue.   I don't think it matters if it's a road, avenue, street, circle, or lane — as far as I know, in America, we always live on a street. Does it vary in British English, or is it always in? If it varies, what are the rules? I inherited a project using SQL Server 2005.  Recently there were some performance problems and I started looking at the indexes, and found  _dta_index_survey_25_135059617__K1_K10_K19:     id ASC, sent_date ASC, group_id ASC   and  _dta_index_survey_21_364632442__K18_K1_K2_K9:     group_id ASC, id ASC, campaign_id ASC, sent_date ASC   which appears to be generated by some kind of automatic performance tuning tool.  I think SQL Server comes with something like that but I'm not familiar with it.  Anyway, id is the primary key, and what I'm trying to understand here is how it could possibly be beneficial to include the primary key within a secondary index... because you have to have the leftmost pieces of information to use an index and if you know id then you've got the row anyway.  Can someone explain why a tool would have generated these indexes and if there's any point in keeping them?  Just because the indexes are getting used doesn't mean they're a good design.  SQL Server is using the wrong indexes lately, and I'm trying to determine why. More specifically, queries against this table that ran in milliseconds a month ago are now taking multiple seconds.  The table is huge (4M rows), and growing steadily, but at the same pace it's been going at for years.  Almost every query joins across group_id or campaign_id.  Often both.  The application almost never specifically selects or sorts by the PK, but I could see how ID could be useful when comparing or merging lists of IDs within the database engine.  ... But id is also an identity column, and an index holds lists of row ids, so it still seems redundant to have the ID in the key when it's also in the index "buckets".  And the additional fields could still be covered by the index without being part of the key.  I discovered that (id, sent_date, group_id) hardly ever gets read.  Meanwhile (group_id, id, campaign_id, sent_date) is one of the hottest indexes.  Next I found that an index which I thought was pretty reasonable (campaign_id, sent_date, group_id, id) also has a index_columns_include of every other column in the table, and occupies more space than the primary clustered index on id!  (but it's also pretty hot...)  Surely I can replace it with a simple (campaign_id, sent_date, group_id)? Differential equation $y''=\frac{y'}{2\sqrt y}$ Exclamation(!) turned in to question mark(?) in title field I just submitted a question () with an exclamation (!) at the end of the title (with one space between the word and the exclamation) but it turned in to question mark (?).   I removed the space between the word and the exclamation, then it shows normal.   Is this an intended feature? I'm writing my final report in LaTeX for my bachelor's degree. I'm aiming at having a document similar to the .doc template used normally.   I want to have my customs headers and footers applied on pages when I'm starting a new chapter.  I'm using documentclass report with fancyhdr and lastpage packages.  My headers are defined like this:  \lhead{\myTitle} \rhead{\today} \cfoot{\thepage\ of \pageref{LastPage}}   My chapters are created using standard \chapter{title} macro.  On pages with new chapters, the only headers/footers I see is the standard page number at the bottom.  What should I do?  EDIT: I've finally gone with Peter Breitfeld's solution. I'Ve gone a step further and created my own chapter command:  \newcommand{\myChapter}[1]{     \chapter{#1}     \thispagestyle{fancy} }   Thanks for the help! This comes from a brain teaser but I'm not sure I can solve it:     You are in a rowing boat on a lake. A large heavy rock is also in the boat. You heave the rock overboard. It sinks to the bottom of the lake. What happens to the water level in the lake? Does it rise, fall or stay the same?   I'd say that the water level drops, because when you drop the stone in the lake, the water level rises according to the volume of the stone, BUT the water level decreases by a volume of water weighting the stone's weight, when you take it off the boat.  Is that correct? I am from a physics background and my mathematics is not very good, so pardon my insolence with the question.  Editing based on the comments : We know that $\pi$ in decimal (i.e. base 10) is transcendental. Is it possible to have a radix base in which $\pi$ can be rational in that base ?  PS : My question is in general for any transcendental number.