what are linux-image-extra and linux-image-generic?
How do I free up more space in /boot?
The following is the first part of Proposition 2.9 in "Introduction to Commutative Algebra" by Atiyah &amp; Macdonald.     Let $A$ be a commutative ring with $1$. Let $$M' \overset{u}{\longrightarrow}M\overset{v}{\longrightarrow}M''\longrightarrow  0\tag{1} $$ be sequence of $A$-modules and homomorphisms. Then the sequence (1) is exact if and only if for all $A$-modules $N$, the   sequence  $$0\longrightarrow \operatorname{Hom}(M'', N)  \overset{\overline{v}}{\longrightarrow}\operatorname{Hom}(M,  N)\overset{\overline{u}}{\longrightarrow}\operatorname{Hom}(M', N)  \tag{2} $$ is exact.   Here, $\overline{v}$ is the map defined by $\overline{v}(f)=f\circ v$ for every $f\in\operatorname{Hom}(M'', N)$ and $\overline{u}$ is defined likewise.   The proof one of direction, namely $(2)\Rightarrow (1)$ is given in the book, which I am having some trouble understanding. So assuming (2) is exact sequence, the authors remark that "since $\overline{v}$ is injective for all $N$, it follows that $v$ is surjective". Could someone explain why this follows?  Given that $\overline{v}$ is injective, we know that whenever $f(v(x))=g(v(x))$ for all $x\in M$, we have $f=g$. I am not sure how we conclude from this surjectivity of $v$.  Thanks! I am designing a poster, which has some geometrical shapes (TikZ paths) surrounded by some text. I would like the text to flow neatly around these shapes. I bet there's some clever TikZ magic that could do this.  EDIT: This is the sort of effect I want, sorry to not be clear:    \documentclass[a4paper]{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (0,0) to (2,-2) to (2,-4) to (4,-4) to [out=up, in=down] (6.5,0); \node [text width=6cm, anchor=north west] at (0,0) { \hspace{5pt}  This is the sort of effect I want to \\ \hspace{23pt} achieve, with text automatically \\ \hspace{36pt} constrained by some \\ \hspace{46pt} geometrical form. Here \\ \hspace{55pt} it's just a curve, \\ \hspace{57pt} but this could \\ \hspace{57pt} also be the \\ \hspace{57pt} text label \\ \hspace{57pt} of a node.}; \end{tikzpicture} \end{document} Why does light of high frequency appear violet? Is there a --parents option for mv like for cp? cp has a useful feature --parents that allows a file's directory structure to be copied to another directory:  $ cp -v --parents source/directory/from target/ ‘source/directory/from’ -&gt; ‘target/source/directory/from’   How do I similarly move a file? Importing google-play-services lib into Intellij IDEA 12 (and 13) Partition of circumference into $3k$ arcs The following problem is from 1982 Russian Mathematical Olympiad. If you go to this , and scroll down to the section Russian Math Olympiad, then this is Problem 333 in that text-file.     Let $k$ be a positive integer. There are $3k$ points marked on the circumference. They divide the circumference onto $3k$ arcs. Some $k$ of arcs have length 1, other $k$ of them have length 2, the rest $k$ of them have length 3. Prove that some two of the marked points are the ends of one diameter.   I haven't given too much thought into the problem yet (I probably wouldn't get anywhere), but I thought I would share this awesome problem.   Added. Trivial Observation: The length of the circumference is $k+2k+3k=6k$. How can I set desktop defaults for new users? How can I set up desktop defaults, much like most distributions do, for every new user? (ex. default wallpaper, apps, etc) Save Illustrator as PDF with transparent background What is the best way to call a script from another script? It seems like to deleted too much files by rm -r and now I have the error of "the system is running a low-graphic mode" in Ubuntu and I have to work in Windows because of that.  However I can load it in recovery mode. I need to copy the files from Downloads folder to a flash drive. Downloads folder has them as I can see by ls command.   When I plug in a flash drive, there will be some messages saying that everything is ok (as I understood) and it's plugged. But when I go to /media/my_name and do ls then I don't see anything. I don't see anything in /run/media/my_name either(I'm not sure if should though).  I can't connect to the Internet for some reason. Ubuntu was installed by wubi.exe file.  How do I save the content of my Downloads folder to a flash drive? Android Seekbar with two thumbs PHP MySQLi doesn't recognize login info Cannot add custom launcher to Ubuntu Dock ('Add to Favorites' option does not show up) I have a custom .desktop file: [Desktop Entry] Type=Application Terminal=false Icon[en_US]=/home/alex/bin/idea-IC-173.4127.27/bin/idea.png Name[en_US]=IntelliJ Exec=/home/alex/bin/idea-IC-173.4127.27/bin/idea.sh Name=IntelliJ Icon=/home/alex/bin/idea-IC-173.4127.27/bin/idea.png  Output of ls -lha .local/share/applications/intellij.desktop: -rwx--x--x 1 alex alex 248 Dez 30 10:54 .local/share/applications/intellij.desktop  Answers posted to a previous question () don't work for me. I can find this launcher in Activities and I can double click on that file and IntelliJ will start. Nevertheless, I cannot add this launcher as a favorite to the dock. The option does not show up. Creating compressed GeoTIFF with QGIS Clipper tool? I have a geo-tiff created by Pix4D which is about 375 Mb in file size.   I have clipped it to a smaller area using Qgis 2.8(using Raster ‣ Extraction ‣ Clipper), and the output file is about 900 MB in size.  Why did the clipping process generate such a large file, when the source file was smaller?   How do I run the clipper tool so that it produces a smaller size? On which Stack Exchange site should I post subjective questions? Iterate until condition is met Symbolizing using RGB values from Excel in ArcGIS Desktop? I have an excel file with 2 attribute columns, 1-feature info 2-Number of color (RGB) that the current feature should be symbolize. This file file can be joined with the layer using the "feature info" field which is unique (join by attribute table). So i have as attribute the color number attribute for every polygon feature.  How can  i use this this information to symbolize every feature with their attributed color already imported from the excel sheet? I'm being asked to find 2 subgroups of $S_3$, one of which is normal and one that isn't normal. I guess, to find the non normal subgroup is easier. I would do this by trial and error, but since the group is $S_3$ and easily visualizable, I guess that there should be a geometrical property that makes it easy to find a normal subgroup. Any of you guys know one? Or should I try this by brute force? I've seen a couple questions around here like , which mentions:     Unfortunately that same browser won't allow me to test HTTP PUT, DELETE, and to a certain degree even HTTP POST.   I've also heard that browsers support only GET and POST, from some other sources like:        However, a few quick tests in Firefox show that sending PUT and DELETE requests works as expected -- the XMLHttpRequest completes successfully, and the request shows up in the server logs with the right method. Is there some aspect to this I'm missing, such as cross-browser compatibility or non-obvious limitations? Looking for way to copy first line of text file to end of every line