Rows of a Matrix is divisible by 19, show that its Determinant is also divisible by 19
On determinants and common divisors
Why did my windshield freeze instantaneously? I want to use an old drive as a secondary hard drive without reformatting. But this old hard drive contains my old Vista installation which takes up gigs of space.  I tried changing ownership and it works to some extent but I can not delete anything in Windows/System32 folder.  Is there an easy way to change permissions so I can delete everything?    The solution is to use Takeown as Wil suggested and use cacls to take full control of the files. Since cacls doesn't seem to be recursive, I fired up cygwin and ran this command to recursively change all the files:  for d in $(find directory-of-interest -type d);do   cacls $d'/*' /e /G username:F; done   where directory-of-interest is in my case /cygdrive/g/Windows and username is my username.  I had to manually run it on directories that had spaces in its name. But after all this, I can now delete the directory. Warning: it seems to me that cacls can potentially royally screw things up if improperly used. I want to prove that $\lim_{(x,y)\to (0,0)} \frac{\sin(x+y)}{x+y} = 1$  Is it sufficient to say that if $u = x+y$ then as $(x,y) \rightarrow (0,0)$ then $u \rightarrow 0$ and then evaluate $\lim_{u\to 0} \frac{\sin u}{u}$ which is 1 by L'Hôpital's rule?  I feel that this is somehow "cheating" and I would really like to prove it in a more rigorous way, i.e., by using an $\epsilon$ - $\delta$ argument.  I have tried for a long time to use the one variable version and prove that if $0 \lt \sqrt{x^2 + y^2} \lt \delta$ then somehow $0 \lt |x+y| \lt \delta$ and it would follow from the one variable case that $| \frac{\sin(x+y)}{x+y} - 1| \lt \epsilon$. However, because $|x+y| = 0$ when $y = -x$ I am not getting anywhere with this.  Any input on this would be helpful :) What is the relationship between regression and linear discriminant analysis (LDA)? Is there a relationship between regression and linear discriminant analysis (LDA)? What are their similarities and differences? Does it make any difference if there are two classes or more than two classes? Completion of rational numbers via Cauchy sequences Can anyone recommend a good self-contained reference for completion of rationals to get reals using Cauchy sequences? Mod shows up with OP background when viewing deleted comments How to disable all div content My distribution is normal; Kolmogorov-Smirnov test doesn't agree I have a problem with the normality of some data I have:  I've done a Kolmogorov test which says it isn't normal with p=.0000,  I don't understand: the skewness of my distribution =-.497, and the kurtosis =-0,024  Here is the plot of my distribution which looks very much normal ...  (I have three scores, and each one of this scores isn't normal with a significant p-value for the Kolmogorov test ... I really don't understand ) I have 50 servers. I manage them from a central management server on SQL Server 2014 Enterprise Edition. I don't use repository.  I could open a query and get result for each one at the same time. But I want to do it in an automated way, like a job, to collect data from each server and store/handle it locally.  Is this possible and if so, how? Gparted: move extended partition on the left I have some free disk space on the left of my ubuntu (sda5)  What is best solution to extend sda5 ?  I can    copy sda3 or sda5 with dd to bigger disk. delete sda3,5,swap create sda3,5,swap dd original partition.   Not sure how to do it properly.  May be there is a simpler solution. Fixed buffers and interior buffers are not working for a polygon that contains a hole I have an iPhone 5 running iOS 9.1 and a Macbook Pro running Yosemite.  Both devices are set up to sync photos to and from iCloud.  When I take a photo on the iPhone (for further processing on the Macbook), it takes an inordinate amount of time until the photo shows up in the Macbook's photos library - sometimes up to 10-20 minutes. Sometimes it seems to work faster if I quit the Photos app on both devices, and start it again.  I often end up sending myself photos through E-Mail because it's quicker. That seems ridiculous!  Is there a way to force a sync on the iPhone, or to speed up the process some other way? If $a, b, c$ be distinct reals such that $$a + \frac1b = b + \frac1c = c + \frac1a$$ how do I find the value of $abc$?  The answer says $1$, but I am not sure how to derive it. I tried to install Ubuntu 12.10 with the Wubi installer while running Windows, because my PC does not accept my BootCD as a bootable medium.  But Wubi showed me this error:  Ubuntu-Installationsprogramm (X) Ein Fehler ist aufgetreten: Could not retrieve the required disk image files Weiter Informationen finden Sie in der Protokolldatei: c:\users\username\appdata\local\temp\wubi-12.10-rev273.log   What can I do, because I want to get rid of my Windows 7 and use the way better Ubuntu 12.10?  Thanks for your huge answer, now my next problem after trying to install wubi with the .iso is, that the same error shows up again and i am not shure which part of the errorreport you need.  Can you tell me? Because i'm not that good at linux. Can one attack for damage after having grappled an opponent? The grappling rules sure are... light. Supposing one has an Extra Attack:   Assuming one has successfully grappled an opponent with one's first attack, can one then perform a normal attack action with one's Extra Attack? Against the grappled opponent or any opponent within reach? Limitations on weapons (e.g. one-handed only)? Assuming one has successfully grappled an opponent with one's first attack, can one's grappled opponent (now with move 0) perform a normal attack action? Against you or against any one in reach? Do advantage and disadvantage (along the lines of restraint) come into play? Are there grappling-specific attacks for damage (e.g. choke-hold)? There are no interfaces on which a capture can be done This is a hypothetical question about how a CPU operates. If I purchase two identical CPUs, and use one long term (say one year), will it be identical in speed to the unused CPU? Will the number of clock cycles, latency of requests, etc on the used CPU be less than that of the unused CPU?  A supporting argument may be that mechanical devices degrade over time, While a CPU has no moving parts (other than the external fan), it does have circuits that can be damaged by heat, and voltage spikes. Lets say that after a year of intensive use, the circuits degrade and fewer electrons can pass since the pathway is narrower, etc.   Is this the nature of how a CPU operates, or is it simply working or broken, with no speed degradation in between? Normal subgroups of dihedral groups Do separate autofocus motors exist for entry level Nikon DSLRs? Plot $|z - i| + |z + i| = 16$ on the complex plane