Prove determinant of $n \times n$ matrix is $(a+(n-1)b)(a-b)^{n-1}$?
Determinant of a specially structured matrix ($a$'s on the diagonal, all other entries equal to $b$)
Substituting table salt or sea salt for kosher salt? The roasted chicken recipe I'm following of course calls for kosher salt, but I don't have any, and getting some is out of the question.  I have sea salt and table salt on hand.  Can I substitute one of those instead, and if so, what is the proper ratio of the kosher salt the recipe calls for to either sea salt or table salt? What is a terminal? How do I open a terminal window? How do I use the terminal? Year-Round Hats for Fun and Profit QGIS update from 2.14 to 2.16 failed on Ubuntu 14.04 Until yesterday my whole qgis and python-qgis worked fine with version 2.14 under Ubuntu 14.04. After a simple sudo apt-get update and sudo apt-get upgrade qgis failed to update... Several attempts to reinstall it with different versions failed.  Current error message (for version 2.14.3) goes like this:  qgis-providers (2.14.3+dfsg-2~trusty1) is configured ... /usr/lib/qgis/crssync: symbol lookup error: /usr/lib/libgdal.so.20: undefined symbol: GEOSDelaunayTriangulation_r   I also tried to reinstall all gdal libraries - not sure if I got all?!  Maybe it is somehow related to this one:  ?  UPDATE:  Trying to install version 2.16.0 it gives different but similar error:  /usr/lib/qgis/crssync: symbol lookup error: /usr/lib/libqgis_core.so.2.16.0: undefined symbol: GEOSNearestPoints_r   UPDATE Sources:  For version 2.16.0 there are these sources in /etc/apt/sources.list:  deb http://qgis.org/debian trusty main deb-src http://qgis.org/debian trusty main deb http://qgis.org/debian trusty main deb-src http://qgis.org/debian trusty main   which are all the same, right?   When I do apt-cache policy qgis it gives me:  qgis:   Installiert:           1:2.16.0+20trusty   Installationskandidat: 1:2.16.0+20trusty   Versionstabelle:  *** 1:2.16.0+20trusty 0         500 http://qgis.org/debian/ trusty/main amd64 Packages         100 /var/lib/dpkg/status      2.0.1-2build2 0         500 http://de.archive.ubuntu.com/ubuntu/ trusty/universe amd64 Packages ffmpeg is not even cutting this and other mp4s to the nearest second Update Manager is constantly offering me updates (e.g. security fixes, updates from PPAs).  How can I tell my Ubuntu installation to automatically download and install updates whenever they become available? Understanding the definition of the order of an entire function in Ahlfors's Complex Analysis Let $f: \mathbb C \to \mathbb C$ be an entire function. The order of $f$ is defined by $$\lambda=\limsup_{r \to \infty} \frac{\log \log M(r)}{\log r}, $$ where $$M(r)=\max_{|z|=r} |f(z)| .$$  Ahlfors in his Complex Analysis claims that     "According to this definition $\lambda$ is the smallest number such that       $$M(r)\leq e^{r^{\lambda+\varepsilon}} $$ for any given $\varepsilon &gt; 0$ as soon as $r$ is sufficiently large."   Why is this true?  My attempt:  We know that $$\lambda=\lim_{\rho \to \infty} \sup_{r \geq \rho} \frac{\log \log M(r)}{\log r}. $$  From the definition of the limit we have that for any $\varepsilon&gt;0$, there exists some $\rho_0&gt;0$, such that $$\left\lvert \sup_{r \geq \rho} \frac{\log \log M(r)}{\log r}-\lambda \right\rvert \leq \varepsilon ,$$ for every $\rho \geq \rho_0$. In other words $$\frac{\log \log M(r)}{\log r} \leq \lambda+\varepsilon $$ for every $r \geq \rho_0$. From here it is easy to see that $$M(r)\leq e^{r^{\lambda+\varepsilon}}, $$ for all $r \geq \rho_0$. I cannot see why $\lambda$ is the smallest number with this property.  Thanks in advance. If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$. Exercise 11, page 45 from Hungerford's book Algebra.     If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every   subgroup of $H$ is normal in $G$.   I am trying to show that $a^{-1}Ka\subset K$, but I got stuck. What I am supposed to do now?  Thanks for your kindly help. Where to place 'only' relative to prepositions? I know that questions about the placement of 'only', are often asked here; accordingly, I searched for an answer to my question before posting it.  Question  Where are focusing adverbs placed relative to prepositions?  For example,   For his presentation, he needed to talk only about tomatoes. For his presentation, he needed to talk about only tomatoes.   My Attempt to Answer the Question  In both examples, it seems to me that 'only' is placed close enough to what it is intended to modify (the topic of the subject's discourse: tomatoes) that I cannot see any justifiable misinterpretations.  One of the examples sounds better to me, but at this point in my studies, I am more interested in what the traditional rules of grammar require, than in how the wordings sound. I know someone who just got an Atrix 4G and previously had an iPhone 3GS. I was asked how he could move his contacts from the iPhone/iTunes onto the Android device. I have never owned an iPhone and have had limited interaction with them. Does anyone know the simplest method of getting iPhone contacts onto an Android device? Combining Shimano RS500 crankset with Stages Shimano 105 5800 I've been thinking about getting a power meter for a while now. I finally decided I would get one, but now I realise that Stages only starts at the Shimano 105 level.  I currently have a Shimano RS500 Crankset ( 50 x 34 ) and I'm very pleased with it, so I don't feel a need to replace the whole crankset with a 105 5800.  I also have no plans to upgrade anytime soon to Dura Ace or something like that (the rest of my bike has the 105 5800 set), so I don't think I should buy a higher lever crank arm from Stages.  Now, I know something about bikes, but not a lot. It seems that what I have (RS500) looks compatible with the 105 crank arm (just judging by the looks), but I would like to be certain before I spend this amount of money.  My set:  Stages I would like to get:   Kind regards and thanks in advance, Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a < 23$. Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a &lt; 23$.  I've tried to combine corollaries of Fermat's little theorem and various other methods to solve this, but have always been stuck. Looking at moving my laundry upstairs, and the right answer is to combine two adjacent closets to get the width and move one of their walls a foot or two into the kitchen to get the depth.  The kitchen floor is 10-inch-square tiles. It would be sort of nice if that continued on into the laundry closet. I do have a full bundle of spare tiles in the basement.   Question: Could/should I plan on the new wall coming in on top of the existing tiles (presumably having to drill to secure the footer without shattering them), or should I plan on removing the ones under the footer and fitting cut pieces back in afterward? Capitalizing "the" when mid-sentence in a company name? Consider a company called:     The Association of Examples Ltd.   When you refer to this company, should you have to capitalize "the" when it's mid-sentence and would have been used even if it wasn't in the name?   It looks odd to me:     In other news, The Association of Examples announced that...      Sarah is the founder of The Association of Examples and has...   But I imagine it's the correct way.  For the grammar-conscious, why or why not?    To give you context, I am asking also when branding ones own company like that. The Economist did it (as did ) and , but I can imagine it can cause confusion. I'm in Belgium (french part) and I cannot find the proper keyboard layout in Settings > Region and Languages > Input Sources.  the closest I found is the french (AZERTY) one but for the symbols such as ! and _ it's not the same keys...  what can I do to solve it ?  Thank you. Which Windows 7 log file contains device connection/disconnection information? Windows 7 frequently plays the usb/new device connection/disconnection sound. It happens both when the computer is idle and under load. All usb device connections have been checked (though I can't rule out a bad cable yet). I thought a good way to track down the issue would be to wait for the sound and then check the log file for the latest connected/disconnected device. I just need to know which log file has this information.  Edit: I'm going to leave the answer accepted, however the issue persists. I get that sound seemingly randomly throughout the day. Anyone else have any ideas? Is there a word for saying "um" or "uh", etc, during speaking?  Or a word for "um" and "uh", etc? How do you minimise hand washing between every step to keep tools clean? Say you cooking beef steak:  You have to unwrap the beef from its packaging, lay it down, get blood on your hands, wash hands, sprinkle salt, wash hands, grind pepper, rub the seasoning into the beef, wash hands, grab the tongs etc..  Is it normal to wash hands after every step or is there a trick to avoid getting all the tools dirty?  If you watch TV, they don't ever wash as much as I do. Text not very readable on different image backgrounds I've come here seeking for a bit of design help or advice on how I could possibly improve the following:  Like the title says, I'm having a website banner with multiple text displayed on different images as backgrounds. Now, since most of the images are dark, I've set the font color as white. But even then, some of the text is not very readable on a couple of images like:    Since I'm working with CSS, I've tried different options such as:  Adding Text Shadows:    CSS:  text-shadow: 3px 3px 0px #000;  Also tried, creating a semi-transparent box around the text:      I feel the box one looks out of place.  I've created a  for anyone who knows CSS. If not, please feel free to advice me based on your imagination alone.  PS: You could also advice on using a different font if that would help it stand out better. Why has Steve Nash moved to the LA Lakers in sign-and-trade deal? Congratulations to Steve Nash on his move to Lakers !  His contract with the Suns has expired so I don't understand why he moved in a sign-and-trade deal.    Why resign and move in trade? Why didn't the Lakers sign Nash without any trade?