Solving System of equations and L-U decomposition of matrices
When does a Square Matrix have an LU Decomposition?
How can we prove that every odd perfect square is congruent to $1$ modulo $8$? How can I run Debian stable but install some packages from testing? Say you're running a server and you don't want to upgrade to Testing (Squeeze) from Stable (Lenny) to just install a required package or two.  What's the best way of installing only certain packages from Testing? Is there any difference in meaning between 'efficacy' and 'efficiency'? There was a foolish (in my opinion) question asked on Scifi.SE       James bond keeps returning with a different face, albeit usually a similar one, and often operates with high-tech gadgetry that seem to be on par with the Doctor's sonic screw driver.   In my opinion each new actor represents a reboot of the franchise using the new face, not a continuation of the story.   Is there any continuity between versions of James Bond which change actors? I'm not talking about characters like M or Q, I'm talking about events or past advisories being referenced in a different Bond movie where the main actor was someone else. Where can I buy an Ubuntu Phone? I need to buy an Ubuntu phone, where can I buy it? It is unavailable everywhere. Is it possible to recover original content from an edited image file? OK possibly a random question here, but one that is relevant to the site and regarding a hot topic nowadays: privacy.  If I load an image file (in my case a PNG photocopy of a document which contains some personal details) into Gimp, and I 'fill' with black (i.e. as if to redact) the areas of the image that contain sensitive information, and I then overwrite the original file, is there any way that the original untouched image can be recovered or gleamed? Such as low level bit analysis or...?  If so what tools and techniques are behind that, and how can I mitigate this? Is it a simple case of not overwriting the original but simply creating a new file with the changes? Plain integer partitions of $n$ using $r$ parts Division of number $n$ on parts $a_1,...,a_r$ where $a_1 \le ... \le a_r$ we call a plain if $a_1 = 1$ and $a_i - a_{i-1} \le 1$ for $2 \le i \le r$. Find enumerator (generating function) for plain divisions.  my try  The hint was to use bijection between plain divisions and some commonly know enumerator. I tried to use enumerator of divisions on different parts: $$ (1+x)(1+x^2)...(1+x^r)$$ where number of plain divisions is  $$[x^n](1+x)(1+x^2)...(1+x^r) $$ let function  $$f(n,r) = [x^n](1+x)(1+x^2)...(1+x^r) $$  For some first divisions it works. For example: $$f(4,3) = 1 $$ $$f(6,3) = 1 $$ $$f(11,5) = 2$$ But when I tried to find bijection, I failed. I found that this function isn't correct because $f(15,6) = 4$ but should be equal to $3$ because: $$15 = 1,1, 2, 3, 4, 4 \\ 15 = 1, 2, 2, 3, 3, 4\\ 15 = 1, 2, 3, 3, 3, 3 $$. There I stucked. Using Windows 10, I can't run certain commands from PowerShell but they all work correctly using cmd. PowerShell: node --version: node : The term 'node' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try again. At line:1 char:1 + node --version + ~~~~     + CategoryInfo          : ObjectNotFound: (node:String) [], CommandNotFoundException     + FullyQualifiedErrorId : CommandNotFoundException  node.exe --version: no output. node.exe: opens a new black console (node.exe application itself). Get-Host | Select-Object Version: Version ------- 5.1.19041.906  Get-Command node: The term 'node' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try again. At line:1 char:1 + Get-Command node + ~~~~~~~~~~~~~~~~ + CategoryInfo : ObjectNotFound: (node:String) [Get-Command], CommandNotFoundException + FullyQualifiedErrorId : CommandNotFoundException,Microsoft.PowerShell.Commands.GetCommandCommand Get-Command node.exe: CommandType Name Version Source ----------- ---- ------- ------ Application node.exe 14.16.1.0 C:\Program Files\nodejs\node.exe $env:Path output has nodejs &amp; git &amp; other paths. cmd: everything works fine with any command. I have git and nodejs in my PATH env variable. What's wrong with PowerShell, what a strange behavior is this and how to fix it? How to run a program without typing the full path? System utilities such as ls don't need to have the full path typed before executing them. However, to execute Netbeans, I have to type /home/chris/netbeans-7.0.1/bin/netbeans. How can I make it so that I only have to type netbeans? It seems Microsoft has tried to solve this problem .  In Windows 7, there is no boundary between monitors and the mouse can move freely across the top of the screen between my 3 monitors, provided I had set their heights equal in display settings. Windows 8 introduced sticky corners. See .  Windows 10 got sticky corners as well. There are a few pixels at the top corners of each display where the mouse cannot cross over onto the other display. One must move the cursor down to avoid this region in order to get to the next display.  The image shows roughly the region where mouse movement is not permitted in Windows 10, but is allowed in Windows 7.    Personally, I had no problem with unrestricted mouse movement across the top of my screens - I got used to "aiming" for the x, and the convenience of unrestricted cursor movement. Like all the people who wanted to disable it in W8, I'm wondering if there is a way to disable it in W10.  Edit to address possible duplicate:  Although the problem is identical to the one in , solutions to solve the problem in W8 involving editing the registry key MouseCornerClipLength do not work in W10, since that registry key is not present in W10. Also adding that key and setting the value doesn't work. I searched the entire registry and couldn't find it in another location. No other W10 keys in the node referenced in the W8 solution are obvious replacements.  Edit to address possible solutions in comments  harrymc's  and  that worked for for Windows 8.1 do not work in Windows 10. How to prove the midpoint of a chord is also the midpoint of the line segment defined by the points of intersection of other two chords with it? This picture is a part of a table i am using, the terms subcases are vertically written but i cant center them vertically also in the next columns terms like A, B, etc are also not vertically centered. I made this table using tabulary package a. My code is  \begin{table}[H]  \centering  \caption{Saturation Table}  \label{tab:5}%  \begin{tabulary}{1\linewidth}{J J J J J J J J J J J J J}  \toprule  &amp; \textbf{Method} &amp; \multicolumn{1}{c}{\textbf{Parameters}} &amp; \textbf{Step 0} &amp; \textbf{Step 1} &amp; \textbf{Step 2} &amp; \textbf{Step 3} &amp; \textbf{Step 4} &amp; \textbf{Step 5} &amp; \textbf{Step 6} &amp; \textbf{Step 7} &amp; \textbf{Step 8} &amp; \textbf{Step 9} \\  \midrule  \multirow{4}[4]{*}{\begin{sideways}\textbf{Subcase A}\end{sideways}} &amp;  \multirow{2}[2]{*}{\textbf{A}} &amp; \textbf{No} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; \textbf{6} &amp; &amp; &amp; &amp; \\[1mm]  &amp; &amp; \textbf{Maximum Saturation {(\%)}} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 4 &amp; \textbf{5} &amp; &amp; &amp; &amp; \\  \cmidrule{2-13} &amp; \multirow{2}[2]{*}{\textbf{B}} &amp; \textbf{No} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; 6 &amp; 7 &amp; \textbf{8} &amp; &amp; \\[1mm]  &amp; &amp; \textbf{Maximum Saturation {(\%)}} &amp; 6 &amp; 6 &amp; 7 &amp; 8 &amp; 9 &amp; 9 &amp; 19 &amp; \textbf{8} &amp; &amp; \\  \bottomrule  \end{tabulary}%  \end{table}% I declared random list using TikZ package and can get items randomly. But at same time I need to get all items in sequential order. How can I do it? Is it possible print \mylist items declared in noncomma variat?  \documentclass[a4paper,14pt]{extreport} \usepackage{tikz}   \def\mylist{{one}{two}{three}{four}{five}}   \pgfmathdeclarerandomlist{mynum}{\mylist} %Define the list   \begin{document} \pgfmathrandomitem{\mynum}{mynum} \pgfmathresult~\mynum\\  \pgfmathrandomitem{\mynum}{mynum} \pgfmathresult~\mynum\\  \pgfmathrandomitem{\mynum}{mynum} \pgfmathresult~\mynum\\  \pgfmathrandomitem{\mynum}{mynum} \pgfmathresult~\mynum\\  \pgfmathrandomitem{\mynum}{mynum} \pgfmathresult~\mynum\\ \end{document} Check synchronously if file/directory exists in Node.js Every element of a group has order $2$. Why, intuitively, is it abelian? How can I install Ubuntu encrypted with LUKS with dual-boot? The Ubuntu installation disk has an option to install Ubuntu encrypted using LUKS. However, there is no option to perform an encrypted installation along-side existing partitions for a dual-boot scenario.  How can I install Ubuntu encrypted alongside another partition from the live disk? What's the purpose of the CIL nop opcode? I'm going through MSIL and noticing there are a lot of  instructions in the MSIL.  The MSDN article says they take no action and are used to fill space if the opcode is patched. They're used a lot more in debug builds than release builds.  I know that these kinds of statements are used in assembly languages to align later instructions, but why are MSIL nops needed in MSIL?  (Editor's note: the accepted answer is about machine-code NOPs, not MSIL/CIL NOPs which the question originally asked about.) Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$ Do you know an explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$? Using the axiom of choice, every vector space admits a norm but have you an explicit formula on  $\mathcal{C}^0(\mathbb{R},\mathbb{R})$?  A related question is: Can we proved that $\mathcal{C}^0(\mathbb{R},\mathbb{R})$ has a norm without the axiom of choice? I'm using Dataloader to Upsert a Child Account to Parent Account using an external ID.  When the Upsert is complete, the Child overwrites the parent, it's not not connecting the Child Account to the Parent Account.  ((See Answer Below)) Same gravatar is displayed for different users in stackexchange.com filters Same gravatar is displayed for different users in the stackexchange.com , under the Top Network Askers in the right side bar.   The red circled image's source (&lt;img src=) are from   https://www.gravatar.com/avatar/?s=18&amp;d=identicon&amp;r=PG&amp;s=30                                ^   Seems the gravatar id is missing here in the image source.  For an example from the list, the user  gravatar id should be    https://www.gravatar.com/avatar/66c66c4d97a7bc3859a85253f003e1fb?s=18&amp;d=identicon&amp;r=PG&amp;s=30   but it is mapped with   https://www.gravatar.com/avatar/?s=18&amp;d=identicon&amp;r=PG&amp;s=30   which caused the display issue.