How do I perform an LU Decomposition without pivoting?
Is it possible to prevent LUDecomposition from pivoting?
Is doing two PhDs a good path? Given that$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$, find $a_7+a_6+a_5+a_4+...+a_1+a_0$ Given that$$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$$find $$a_7+a_6+a_5+a_4+...+a_1+a_0$$  Is there anyway to do the question without using binomial theorem and expanding the expression on the LHS?? How do I grep for all non-ASCII characters? How does a transformer transmit power from the primary to the secondary? I'm trying to get my head wrapped around transformer operation and in the process regretting the times I snoozed in my Electromagnetics class as a EE student back when I was a lad :)  I'm looking for an intuitive understanding, but not just an analogous one. I'd like it to be grounded in the actual physics of what's happening. I've found several excellent sources on the web, but they all seem to skirt this question.  I've come across a few interesting hints and am now tantalizingly close, I think, but still yearning :)  Fact 1: Although varying sinusoidally, the "peak-to-peak" flux, so to speak, in a transformer's core is essentially constant (for a given voltage applied to the primary), regardless of the load.  My intuitive hypothesis was that variation in the "strength" of the flux was what transferred the energy from the primary to the secondary, but this fact would seem to contradict that theory. I had thought that the primary makes a bunch of flux based on the current flowing through it and the secondary sucks it up to make current of its own. No dice, it seems.  Then of course there's the fact that the formula for flux involves only voltage, time (frequency), and turns :)  Fact 2: The current in the primary is (approximately) 90 degrees out of phase with the voltage at no load, and approximately aligned in phase at full load.  This fact seems very promising and also curiously satisfying. It would imply that the Volt-Amps (VA) of the primary is constant and only the power factor changes as the current load on the secondary increases.  But I still don't get how the energy is actually being transferred. It seems vaguely like the flux is just there as an energy conductor or something and some other phenomenon is actually doing the energy transfer bit.  Can someone see what I'm missing and explain what's actually happening in there? calculate the mean of trials for each subject in R How to really clear the terminal? I can issue the clear command or press Ctrl + L to clear the current Ubuntu terminal, but this just shifts previous output upwards and if you use mouse scroll or PgUP and PgDown keys it's hard to distinguish where the output of previous command ends and output of current command begins.  Is there a way to really clear the terminal so I won't see previous command results? My /boot partition hit 100% and now I can't upgrade. Can't remove old kernels to make room $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$ Let $f:[a,b]\to  R$ be integrable and continuous on $(a,b)$. Prove that: $$\lim_{h\to 0} \int_a^b\frac{f(x+h)-f(x)}{h} \,\mathrm{d}x = f(b)-f(a).$$  What I've tried so far: make a change of variables, which didn't help. I also thought of using the intermediate value theorem inside the integral, but the function being differentiable is not specified. Any help, tips? Thanks in advance! Is it true that a dihedral group is nonabelian? Is it true that a dihedral group is nonabelian?  I'm not sure if the result is true. I checked it for some lower order and I think the result may correct.   But I failed to prove/disprove the result. A known identity of binomial coefficients is that $$ \sum_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}. $$ Is there a combinatorial proof/explanation of why it holds? Thanks. I’m writing a document in the latex and it contains some BNF grammar noations in several places of the documents. (I used verbatim package in order to write these BNF grammar notations)  Now I want to add a new section to the document that shows name of all grammar notation and their page numbers. This should be similar to “List of Figures” page.  I’m new to Latex and your help will be very helpful for me.  Thanks How do I set the default program? How do I set the default program that I use?  I have tried to open System Info → Default Program → change my program, but it won't work,  Any idea? Or should I use Terminal?   I want to replace the default movie player with VLC media player, because the current movie player is useless to me. Calculate difference between two dates (number of days)? How do I remove the OneDrive folder from my File Explorer folder tree in Windows 10? I don't use or want to use OneDrive, but after upgrading to Windows 10 it's been installed automatically and added to the sidebar of every explorer window:    I can't seem to figure out how to get rid of it. I can't uninstall it like a normal app, and I can't seem to unpin it in Explorer's options.  I tried following  to getting rid of it, but that seems to only remove stored OneDrive files.  I've also tried following another  and , but I can't seem to edit group policies on my computer (maybe because I upgraded from Win7 Home Premium?).  All I would really like is to be able to remove the OneDrive shortcut from my explorer sidebar, though being able to uninstall OneDrive would be a bonus.  I'm not sure what I should try now. Is there a way to remove OneDrive from Windows 10? I need to calculate the following indefinite integral:  $$I=\int \frac{1}{\cos^3(x)}dx$$  I know what the result is (from Mathematica):  $$I=\tanh^{-1}(\tan(x/2))+(1/2)\sec(x)\tan(x)$$  but I don't know how to integrate it myself. I have been trying some substitutions to no avail.   Equivalently, I need to know how to compute:  $$I=\int \sqrt{1+z^2}dz$$  which follows after making the change of variables $z=\tan x$. How to change password complexity requirements in Ubuntu 14.04LTS What is the difference in meaning among these sentences? Walking is good exercise. Walking is a good exercise. Walking is a good form of exercise.     I'd like to know the difference in meaning among these sentences. Thanks a lot. How could I retrieve the exact duplicate value from conditionally formatted list that highlight duplicates? I have imported a webpage table in to Google Sheets. It frequently being updated. A series of calculations has been conducted on the sheet named Shawn Of the link spreadsheet.  I have filtered the my desired results into the Calculation sheet of that linked document... which is in columns A5:A. I then applied =ARRAYFORMULA(if(A5:A200=&quot;&quot;,,A5:A200*{12,13,37,101,111})) in columns B5. The Results of the formula extends from B5:F. This results from a5:F was subsequently conditionally formatted to highlighted duplicates in the aforementioned, i.e. a5:f using the lists of values in K5:K and I5:5. In Columns A5:F, is it possible to generate/place values in the range A5:f with matching name of states and aligned values in J5:K and H5:I? How can I get apt to use a mirror close to me, or choose a faster mirror? transpose columns to rows