I stumbled upon  question online:  $$A=\begin{bmatrix}5&amp;6&amp;&amp;\cdots&amp;6 \\6&amp;5&amp;6&amp;\cdots&amp;6 \\&amp;&amp;\ddots&amp;&amp; \\6&amp;\cdots&amp;6&amp;5&amp;6 \\6&amp;\cdots&amp;&amp;6&amp;5 \end{bmatrix}\in \mathbb R^{82\times 82}$$  I also found a way to solve this in Chegg:    Is there a better way to solve this problem maybe by reducing it to upper triangular form?
This question aims to create an &quot;&quot;  of numerous questions that ask about determinants of specific matrices (I may have missed a few):              The general question of this type is  Let $A$ be a square matrix of rank$~1$, let $I$ the identity matrix of the same size, and $\lambda$ a scalar. What is the determinant of $A+\lambda I$?  A clearly very closely related question is  What is the characteristic polynomial of a matrix $A$ of rank$~1$?
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$ I can't crack this one.      Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$ (the only constraint is that  $a,b,c,z \in \mathbb{Z}$ and $c\neq 0)$ Find the Unit Vector of a Three Dimensional Vector Why is the Mann–Whitney U test significant when the medians are equal? I've received a results from a Mann-Whitney rank test that I don't understand.  The median of the 2 populations is identical (6.9). The uppper and lower quantiles of each population are:   6.64 &amp; 7.2 6.60 &amp; 7.1   The p-value resulting from the test comparing these populations is 0.007. How can these populations be significantly different? Is it due to the spread about the median? A boxplot comparing the 2 shows that the second one has far more outliers than the first. Thanks for any suggestions. Why does C# disallow readonly local variables? Meaning of 'const' last in a function declaration of a class? How do I drop root privileges in shell scripts? The "--up" option in OpenVPN is normally used for routing etc. And so it is processed before OpenVPN drops root privileges to run as nobody. However, I am invoking shell scripts that need to run as an unprivileged user.  How do I do that? I have studied , especially polynomial's and tylerl's answers, but I do not understand how to implement. I am working in Centos 6.5, and suid is blocked, both as "chmod u+s" and as "setuid()".  There is an OpenVPN plugin ("openvpn-down-root.so") which enables scripts invoked by the "--down" option to run as root. There could be an equivalent, such as "openvpn-up-user.so", but I have not found it.  Edit0  Per Nikola Kotur's answer, I've installed . Although the chpst command works in terminal, in the up script it fails with "command not found". What works is "sudo chpst" plus setting the proper display and language. Please see  Given that, the up script needs these four lines:  LANG="en_US.UTF-8"; export LANG GDM_LANG="en_US.UTF-8"; export GDM_LANG DISPLAY=:0; export DISPLAY sudo chpst -u user -U user /home/user/unprivileged.sh &amp;   Edit1  Per 0xC0000022L's comment, I find that "sudo -u user" works as well as "sudo chpst -u user -U user":  LANG="en_US.UTF-8"; export LANG GDM_LANG="en_US.UTF-8"; export GDM_LANG DISPLAY=:0; export DISPLAY sudo -u user /home/user/unprivileged.sh &amp;   I'll study man sudoers and update if/when I get sudo alone to work. Is it possible to migrate programs from 32 bit Windows to a new 64 bit Windows machine (both Windows 7)? I've got a Windows 7 Pro 32 bit PC. Getting a new Windows 7 Home 64 bit.  Is there anything I can use to transfer my  programs (the ones that don't come in a 64 bit flavor)  to the new PC? There is a related  that doesn't address the programs part. What are copy elision and return value optimization? Use Cauchy-Schwarz inequality to show series convergence How can I determine how much bleed to use? How can I make a camera the active one? Often I see code blocks pasted into questions with no formatting, or terrible formatting.  It's sometimes quite a chore to fix these: you have to either manually space out each line, or paste the code into an IDE, format it there, and paste it back.  Could we have a button/function where you could highlight a code block, and it would turn this:  foreach (var i in stuff) { if (i==1) { Whatever(); } }   into this:  foreach (var i in stuff) {   if (i==1) {     Whatever();   } }   I realise the function would have to work differently based on the language in the code block. Perhaps  it could use the same rules as the prettify code.  Also, it wouldn't be a big deal if it gets the language wrong and breaks the code, since you can always just ctrl+z. What is the best way to globally change the amount of vertical space between items in list environments? Why None is the smallest in python? Workflow for converting LaTeX into Open Office / MS Word Format I often have to write up reports based on the analysis of some data. I use R to analyse the data and export tables, figures, and text. This is then included into a LaTeX document either using input or Sweave ().  However, when I collaborate with others, I sometimes need to provide a document in Open Office / MS Word format.  Question:  Thus, assume the simplest scenario   I have a LaTeX document with text, tables, and figures I need to export this reliably into Open Office or MS Word format: this includes mathematical formulas, table formatting, and quality figures) I don't need to go back from MS Word to LaTeX   What is a reliable, efficient, and preferably free process?  Initial Thoughts:   Export to HTML,  LaTeX - LyX - ODF Use odfWeave  that deals with some specific issues associated with LaTeX to Open Office conversion    I was hoping that there is an expert out there who has worked out a good system already. proving $\left(1+\frac 1n\right)^{n} = 1 + \sum_{k=1}^n \{\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn)\}$ using the binomial theorem Is there any way other than instanceof operator for object type comparison in java? I am currently learning how to use TikZ/PGF to make some figures for a project report, and so I have a question:     Is there is a practical way of making a particular object into a node?   The object I have in mind is shown in the Figure below. I want the object to consist in the big circle, the two circular arcs, the label and anchors at north, south, east and west. The dotted lines are simply there to indicate that I am going to have paths going out of these points, which is why I need the anchors there.     I include the source, in the case that it is useful to anyone.  \begin{tikzpicture} \draw[help lines, gray, dotted] (-2,-2) grid (2,2);  \begin{scope}[shift={ (0,0) } ]     \begin{scope}[rotate=90]         \draw[thick] (-1,0) arc[start angle=-90, delta angle=90, %                               x radius=1, y radius=1] -- (0,1) %NW                      (0,-1) arc[start angle=180, delta angle=-90, %                                    x radius=1, y radius=1] -- (1,0); %SE         \draw[gray] (0,0) circle (1);     \end{scope} % Anchor replacements     \node(N1)       at (0,1)    {};     \node(S1)       at (0,-1)   {};     \node(E1)       at (1,0)    {};     \node(W1)       at (-1,0)   {}; % Label     \node(Crossing number) at (0,0) {1}; \end{scope}  \path[thick, gray, dotted] [ out=90,   in=270]     (N1.center) edge (0,2) [ out=180,  in=0]       (W1.center) edge (-2,0) [ out=270,  in=90]      (S1.center) edge (0,-2) [ out=360,  in=180]     (E1.center) edge (2,0); \end{tikzpicture}   PS. I have had a look at the Manual, but I could not find a description of how to do this. How can I  compare (without calculator or similar device) the values of $\pi^e$ and $e^\pi$ ? update-alternatives --install says it needs link name path priority? I typed:  sudo update-alternatives --install "/usr/bin/java" "java" "/usr/lib/jvm/ jdk1.8.0/bin/java" 1   It's says alternatives --install needs link name path priority