Evaluate the determinant of a rank-1 matrix plus $I$
Find the determinant of $I + A$
Monotonicity of the sequences $\left(1+\frac1n\right)^n$, $\left(1-\frac1n\right)^n$ and $\left(1+\frac1n\right)^{n+1}$ What is the difference between Gödel's completeness and incompleteness theorems? Showing a set is closed under inverses Let $G$ be a finite group, say a group with $n$ elements, and let $\emptyset \neq S \subseteq G$. Suppose $e \in S$, and that $S$ is closed with respect to multiplication. Prove that $S$ is a subgroup of $G$.    Let $G = \{a_1, \ldots, a_n\}.$ Let $a_i \in G.$ Then any number of $a_ia_1, a_ia_2, \ldots, a_ia_n \in S,$ since $S$ is closed under multiplication. One of those $a_ia_j$ is $e$ since $e \in S.$ Then either $a_i$ or $a_j$ is $a^{-1}.$ Would this argument work? I would like to protect myself from unreasonable demands during my work day.  One of those is telling people that I will not respond to any emails before 3pm.  I'd like to set up a rule in outlook that replies to all emails before 3pm with a specific message. I'd like this to be done every day, no matter the date.  How do I set this up?  I've scoured Google best I can so far, and I think, based on a Exchange forum, that a script might be needed for this.  But what I found so far was only server side scripts. I need something on my own machine.  references: How do I get permissions to edit system configuration files? find all the members of A4/K Let K={(1),(12)(34),(13)(24),(14)(23)} show that K is a normal subgroup of the alternating group of degree A4 and find all the members of A4/K and write down the group table for A4/K.   i know that K is the Klein four group and i have already proven it is a normal subgroup but i need a start on approaching the A4/K part of this question no direct answers are necessary,just ideas thank you! :) Three side-by-side tables I am using this LaTeX code to generate three tables side by side. However, it showing errors and not giving satisfactory result. Can anyone please help me to short out the problem.  \begin{table} \centering \makebox[0pt][c]{\parbox{1.2\textwidth}{% \begin{minipage}[b]{0.265\hsize}\centering \begin{tabular}{ | c | c |c | } \multicolumn{3}{c} \hline {$q=1/10$} \\ \hline T &amp; $r_h$ &amp; $\omega$ \\  \hline 0.233 &amp; 0.135 &amp; 2.38486-0.34667I  \\  0.256 &amp; 0.140 &amp; 2.38092-0.35837I \\ 0.273 &amp; 0.145 &amp; 2.38049-0.35982I \\  0.278 &amp; 0.146 &amp; 2.38007-0.36130I \\  0.281 &amp; 0.147 &amp; 2.37964-0.36282I \\  \hline 0.284 &amp; 0.761 &amp; 2.54150-2.03209I \\ 0.285 &amp; 0.765 &amp; 2.54515-2.04292I \\ 0.289 &amp; 0.800 &amp; 2.57799-2.13761I \\ 0.302 &amp; 0.900 &amp; 2.67987-2.40712I \\ 0.312 &amp; 1.000 &amp; 2.79214-2.67552I \\ \hline \end{tabular} \end{minipage} \hfill \begin{minipage}[b]{0.265\hsize}\centering \begin{tabular}{ | c | c | c | } \multicolumn{3}{c} \hline {$q=1/9$} \\ \hline T &amp; $r_h$ &amp; $\omega$ \\ \hline 0.227 &amp; 0.150 &amp; 2.34385-0.41094I  \\  0.245 &amp; 0.155 &amp; 2.34215-0.41723I \\ 0.260 &amp; 0.160 &amp; 2.34056-0.42416I \\  0.271 &amp; 0.165 &amp; 2.33908-0.43175I \\  0.276 &amp; 0.167 &amp; 2.33852-0.43497I \\  \hline 0.280 &amp; 0.720 &amp; 2.50248-1.92299I \\ 0.283 &amp; 0.750 &amp; 2.52893-2.00424I \\ 0.286 &amp; 0.780 &amp; 2.55660-2.08533I \\ 0.289 &amp; 0.800 &amp; 2.57568-2.13931I \\ 0.302 &amp; 0.900 &amp; 2.67807-2.40842I \\ \hline \end{tabular} \end{minipage} \hfill \begin{minipage}[b]{0.265\hsize}\centering \begin{tabular}{ | c | c | c |} \multicolumn{3}{c} \hline {$q=1/8$} \\ \hline T &amp; $r_h$ &amp; $\omega$ \\  \hline 0.246 &amp; 0.180 &amp; 2.29733-0.50611I  \\  0.255 &amp; 0.185 &amp; 2.29654-0.51364I \\ 0.263 &amp; 0.190 &amp; 2.29589-0.52172I \\  0.269 &amp; 0.195 &amp; 2.29534-0.53033I \\  0.273 &amp; 0.199 &amp; 2.29496-0.53758I \\  \hline 0.275 &amp; 0.675 &amp; 2.46067-1.80426I \\ 0.277 &amp; 0.700 &amp; 2.48131-1.87194I \\ 0.288 &amp; 0.800 &amp; 2.57245-2.14170I \\ 0.302 &amp; 0.900 &amp; 2.67555-2.41027I \\ 0.317 &amp; 1.000 &amp; 2.78870-2.67796I \\ \hline \end{tabular} \end{minipage}% }} \end{table} Does there exist a holomorphic function with the following property? Redirect parent window from an iframe action Installing debian package through Synaptic I want to install a .deb file. After going through various questions, I came across these three options: dpkg, GDebi and Ubuntu Software Center. However, I want to install the. Deb file via Synaptic Package Manager only. Is there any method by which I can install. Deb file as well as all it's dependencies via Synaptic Package Manager? Common binaries with support for command execution, like `awk` and `vim`, not respecting setuid bit? If-else working, switch not Exercise on infinite series: pointwise product between convergent serie and unbounded sequence I am not able to solve this exercise. I've tried everything.     Exercise Let be $a_n &gt; 0$ a sequence and suppose that $\sum a_n$ converges. Prove that exists a sequence $c_n &gt; 0$ such that $\lim c_n = \infty$ and $\sum c_na_n &lt; \infty$   I don't even know if I have to find an "always-valid" closed form for $c_n$ (maybe in function of $a_n$?) or prove its existence in another way.  Thanks in advance. Good reasons to prohibit inheritance in Java? What are good reasons to prohibit inheritance in Java, for example by using final classes or classes using a single, private parameterless constructor? What are good reasons of making a method final? What is the difference between “do” and “make”? Logging into Ask LibreOffice with my Stack Exchange OpenID If I'm on , I click on OpenID and then enter  and click Log In, I get a page that says:  An error occurred on the server  This event has been recorded.  If you believe you encountered this message in error, please report it.   I clicked report it and here I am reporting it! Using Firefox 26 how to adapt the sorting of a custom type `@standard` in using biblatex/biber Capillary action and conservation of energy When I dip a paper towel in a cup of water the water gets drawn up due to . How is this reconciled with conservation of energy, as it would seem on the surface that the potential energy of the system has gone up with no work being done? Converting ArcGIS layer style to Styled Layer Descriptor (SLD) file? I am putting together a GIS server using GeoServer and need some help with importing my layer styles from ArcGIS 10 to  format.    I have one layer in ArcMap properly symbolized and labeled, how can I get this layers symbolization and labeling into a SLD file? When to use static classes in C# Here's what :   static class CompanyInfo {     public static string GetCompanyName() { return "CompanyName"; }     public static string GetCompanyAddress() { return "CompanyAddress"; }     //... }       Use a static class as a unit of   organization for methods not   associated with particular objects.   Also, a static class can make your   implementation simpler and faster   because you do not have to create an   object in order to call its methods.   It is useful to organize the methods   inside the class in a meaningful way,   such as the methods of the Math class   in the System namespace.   To me, that example doesn't seem to cover very many possible usage scenarios for static classes. In the past I've used static classes for stateless suites of related functions, but that's about it. So, under what circumstances should (and shouldn't) a class be declared static?