The result of Example 16 suggests that perhaps the matrix   $A=\begin{bmatrix}  1  &amp; \frac{1}{2} &amp; \frac{1}{3} \ \ \cdots \  &amp; \frac{1}{n} \\   \frac{1}{2}&amp; \frac{1}{3} &amp; \cdots &amp; \frac{1}{n+1}\\ \frac{1}{3} &amp; . &amp; \cdots &amp; .\\. &amp; . &amp; \cdots &amp; .\\\frac{1}{n}  &amp; \frac{1}{n+1} &amp; \cdots &amp; \frac{1}{2n-1} \end{bmatrix}$  is invertible and $A^{-1}$ has integer entries. Can you prove that?
Let $n$ be a positive integer. Show that the matrix  $$\begin{pmatrix} 1 &amp; 1/2 &amp; 1/3 &amp; \cdots &amp; 1/n \\ 1/2 &amp; 1/3 &amp; 1/4 &amp; \cdots &amp; 1/(n+1) \\ \vdots &amp; \vdots &amp;  \vdots &amp; \ddots &amp; \vdots\\ 1/n &amp; 1/(n+1) &amp; 1/(n+2) &amp; \cdots &amp; 1/(2n-1) \end{pmatrix}$$  is invertible and all the entries of its inverse are integers. This is an exercise in Hoffman and Kunze's linear algebra book. Any hints will be appreciated!
Getting an "Authentication token manipulation" error when trying to change my user password I am logging in to my Ubuntu Server using my username. Once I am logged in I am typing passwd command. Entering a new password but a second after getting following error messages:  passwd: Authentication token manipulation error passwd: password unchanged   What is wrong here? How can I change my password otherwise if I don't have access to that server physically, i.e. I am connecting remotely with ssh using terminal. T-SQL: How to update just date part of datetime field? How to install apk in 2nd user of android 5.0 without playstore So, android 5.0.2 doesn't allow side loading of apks for 2nd user (irrespective of whether it is guest or standard user). "Unknown Sources" is disabled and is uncheckable. And I use a pure Cyanogen Mod 12 (android 5.0.2) without any Google apps. So, there is no Play Store app.  But I have root access.  As shown in the pics, Unknown Sources is Uncheckable and installation is blocked.  (Click image to enlarge)     With this situation, how can i install apks on to the 2nd user account??  EDIT:   It seems Google intentionally (in the name of security) blocked sideloading apks for 2nd user in android 5.0.2. There is a bug report . And sideloading was reenabled in android 5.1.   I will post how to sideload apks on lolipop 2nd user using adb. If this can be done without adb please post. US Salary Transfered to Indian Acc and Tax Relation I am on an H1b visa working and receiving a salary in the US. I have transferred approximately $15-20k to my account in India Account (not an NRE account).    How would this transfer affect my taxes in US and India. How can I avoid tax on the money that I have transferred. Would any investments help save taxes? Do I need to declare anything? If so, where ? Infinity, is clearly not . But there is some dissent on whether or not zero is finite. I have seen authors use "finite" to indicate the value of $0$ is excluded as well as infinity.  Is there any rule about this? How to find an end point of an arc given another end point, radius, and arc direction? Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$ Suppose $f(x)$ and $g(x)$ are continuous function from $[0,1]\rightarrow [0,1]$, and $f$ is monotone increasing, then how to prove the following inequality: $$\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$$ Where is the denoiser? Test for convergence of the series $\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$ What are the minimum contributions required for co-authorship Mathematics for Quantum Mechanics What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation. How do I list the members of a group? How can I see all the members of a group in Linux? Is it possible to add new alphabets to unicode-math? The Riemann zeta function $ζ(s)$ is defined for all complex numbers $s ≠ 1$ with a simple pole at $s = 1$. It has zeros at the negative even integers, i.e., at $s = −2, −4, −6, ...$.   My question: How one can obtain these roots. Notice these sentences:   Shops are open late in summer.   Summer is a traditionally viewed as a slow season for games.   At the summer solstice, the days are longest and the nights are shortest.   it's time to start thinking about what 2016's Song of the Summer will be.    In English class, they told us that "the" is used for the things that are known.  One example for this was a phrase like "The man who killed his wife".  So when we are speaking of that man, we know what he did. Somehow we know something more than nothing about him. He's not just every man in the world.     So Now I'm confused about why "the" is not used in the first and second sentences. Can anyone please explain it for me? Can't access select https sites on Linux over PPPoE My internet connection used to be a direct LAN connection to my provider. Back then, everything would load fine on both Windows and Ubuntu (dual boot). However, a while ago they started needing me to dial (PPPoE) using a username and password. Gateway, subnet mask, IP, DNS servers all stayed the same. But since then, I haven't been able to browse certain websites on Ubuntu, even though there have been no such issues on Windows. Some example websites are -  (although share.ovi.com loads fine, and nokia.com loads fine),  (works on Chrome(ium) and Opera but not on Firefox (both 3.6 and 4)) Mozilla  and other random websites.  Some of the websites that don't load show timeout messages and for some websites (like the moz addons one), the browser will keep trying to load without an end (I've left it like that even for hours but not noticed anything different happen).  I have tried changing the DNS servers to public ones. I have even tried booting from a Fedora LiveCD and then changing the DNS to those (and even to the ones of OpenDNS), but the exact same thing happens. What could be inherently wrong with some config within Linux itself that is causing this problem?  Does anyone know why this is happening and how it can be fixed?  Note: This question has been  on SU, but not gotten any responses.  Update: Just saw  that someone else was having similar problem and solved it by putting a NetworkManager.conf file in /etc/NetworkManager. What needs to be in that file? How do I escape a percentage sign in T-SQL? How to find out why "context is incorrect"? I have been trying to write my first addon for Blender over the last couple of days. One error I came across quite often is the context is incorrect error for an operation of bpy.ops.  I learned that one can ask the poll function of an operator if the context is correct, but this does not tell why the context is correct/incorrect. What would be the best way to figure that out? Only way I could think of is to look into the code of the poll function. If that is the best way, what is the fastest way to find the appropriate piece of code? Collinearity can pose certain problems in various kinds of regression problem. In particular, it can make the parameter estimates have high variance and be unstable.   Various methods have been proposed to deal with this including ridge regression, partial least squares regression, principal components regression, dropping variables and getting more data.   One method that is controversial is standardizing or scaling the independent variables, with various experts saying it is a good (e.g. Garcia) or bad (e.g. Belsley) idea. Belsley's issue seems to be (in non-technical terms) that changing the IVs just pushes the problem under the rug.  But other experts seem not to agree. And the authors tend to get rather heated in defending their own positions.   Back when I did my dissertation (on collinearity diagnostics) I found Belsley's arguments convincing, but that was long ago (I got my degree in 1999).  I'm looking either for expert guidance or for any current review article that is unbiased. How to compute azimuth between QgsPointV2s? The  class has an azimuth() method but the new  class does not. What's the best way to compute the azimuth between QgsPointV2s? I couldn't find a convenient way to convert V2 to the old version, so my fallback is to construct a QgsPoint from the V2's x and y:   self.traj = QgsLineStringV2(...)     p_i = self.traj.pointN(self.i) # this returns a QgsPointV2 p_j = self.traj.pointN(self.j) a = QgsPoint(p_i.x(),p_i.y()).azimuth(QgsPoint(p_j.x(),p_j.y()))   Is there a better way?