Why does the shortcut for finding inverse of 2x2 matrices work?
Deriving the inverse of a 2x2 matrix
How to find previous boot log after Ubuntu 16.04+ restarts? My question is, how can I find boot log from previous system boot attempt?  Today when first powering on my PC, boot process stopped on Ubuntu logo, when I pressed Esc I have seen several lines containing some kernel error and restart required at the bottom, so I pressed Ctrl+ALt+Del and next boot went OK without problems.  I have trouble finding messages from the screen I have seen during the first unsuccessful boot. Should I have taken picture to my phone?  /var/log/boot is there but empty, I searched  and  for strings I remembered with today's date like error but found nothing familiar to what I have seen on previous boot screen.  $ journalctl -b -1 gives me only kernel messages during boot, I can find that elsewhere too, and they are not what was appearing on screen during boot, journalctl is useless for me, I am looking for messages appearing on screen during boot time.  For now, only option is take a photo of write the message on paper. Statistical significance (p-value) for comparing two classifiers with respect to (mean) ROC AUC, sensitivity and specificity I have a test set of 100 cases and two classifiers.  I generated predictions and computed ROC AUC, sensitivity and specificity for both classifiers.  Question 1: How can I compute p-value to check if one is significantly better than the other with respect to all scores (ROC AUC, sensitivity, specificity)?    Now, for the same test set of 100 cases, I have different and independent feature assignments for each case. This is because my features are fixed but subjective and provided by multiple (5) subjects.  So, I evaluated my two classifiers again for 5 "versions" of my test set and obtained 5 ROC AUCs, 5 sensitivities and 5 specificities for both classifiers. Then, I computed the mean of each performance measure for 5 subjects (mean ROC AUC, mean sensitivity and mean specificity) for both classifiers.  Question 2: How can I compute p-value to check if one is significantly better than the other with respect to mean scores (mean ROC AUC, mean sensitivity, mean specificity)?    Answers with some example python (preferably) or MatLab code are more than welcome. Lost passport with Schengen visa What is difference between a ring and a field? Plotting data seems "noisy" If every element of set A ia an element of set B then we say that A is subset of B. A is said to be proper subset if A does not equal B.  My question is - whether the symbol we use to show subset is  same as that for proper subset? I have seen that A is subset of A itself is shown by the same symbol as that for the subset while when we write improper subset, we usually write equal to sign with symbol of subset. So, please help me to know this. How did Harry become a Horcrux? To make a Horcrux, certainly murder can't be the only requirement. It is obvious a proper spell is needed for completing a Horcrux. Voldemort could have made a thousand Horcruxes, as he had already murdered a thousand people. But, how on earth did Harry become a Horcrux, with Voldemort murdering his mom and not using the Horcrux-making spell? Certainly Avada Kedavra is not the spell used for making a Horcrux. Should outdated answers be voted down? On Stack Overflow, there are many questions that relate to currently-developing technologies such as HTML5 and CSS3. The accepted answers to these questions may become outdated, and better answers may appear. However, because the answers are accepted, it is likely that they will continue to be upvoted by users reading the answers, and the OP will likely not notice that a better, more up-to-date answer may exist.  Should these outdated answers be voted down? If not, what should we do with them? Nicomachus theorem proof - what did I do wrong? The exercise asked me to proof $1^3=1$ $2^3=3+5$ $3^3=7+9+11$ $...$ I formulate the equation as (1)$$a^3 = \sum_{i=0}^{a-1} (a-1)a+1+2i$$ Proof base case: $$1^3=\sum_{i=0}^{1-1} (1-1)(1)+1+2i=1$$ Proof (a+1) case: (2) $$(a+1)^3=a^3+3a^2+3a+1$$ (3) $$(a+1)^3=\sum_{i=0}^{(a+1)-1}((a+1)-1)(a+1)+1+2i=\sum_{i=0}^{a}(a)(a+1)+1+2i$$ factor out last summation term, so number of iterations match (1): $$\sum_{i=0}^{a-1}[(a)(a+1)+1+2i]+(a)(a+1)+1+2a=\sum_{i=0}^{a-1}[(a)(a+1)+1+2i]+a^2+3a+1$$ rearrange the summation term, so part of equation match (1): $$\sum_{i=0}^{a-1}[(a)(a-1)+1+2i]+\sum_{i=0}^{a-1}(2a)+a^2+3a+1$$ substitute summation with (1): (4) $$a^3+\sum_{i=0}^{a-1}(2a)+a^2+3a+1=a^3+(2a)(a-1)+a^2+3a+1=a^3+3a^2+a+1$$ From (2) I got $a^3+3a^2+3a+1$ but from (3) &amp; (4) I got $a^3+3a^2+a+1$ My result with induction is off by 2a. Can someone please help me to understand where I did wrong? Wifi hotspot software package other than ap-hotspot? I have tried using ap-hotspot to create a wifi-hotspot but it gives me some problem every time I use it . I just want to ask is there any other software  package that create a wifi-hotspot othen than ap-hotspot ? There's a story my grandpa use to tell me when I was younger, about the sole survivor of of an attack on a mining vessel in space. The man lives in space for months/years, ignored by the company he worked for and never rescued. Then when he thinks he is being rescued, it's actually another set of raiders who attack him and kidnap him.  He then wakes up in captivity in some sort of prison inside of an asteroid, and has a word tattooed on his forehead. My grandpa called him Ronin (that's what the tattoo on his forehead said) but I don't know what the character's real name is. Anyways, he learns that he has the ability to teleport after having a brush with death and decides to make his way back to Earth so that he can exact revenge on the mining company who abandoned him and left him floating to die.  Does anyone know what this story or book may be? My grandpa told it to me when I was little, he said that he got it from a book he use to love reading when he was younger. I'm assuming the book is very old (possibly pre 1940's as he was born in the 20s). I can't ask him as he is no longer alive. I'm also unsure as to whether or not all the details in the story he told me, are the same as in the original. How does a uniform prior lead to the same estimates from maximum likelihood and mode of posterior? I am studying different point estimate methods and read that when using MAP vs ML estimates, when we use a "uniform prior", the estimates are identical. Can somebody explain what a "uniform" prior is and give some (simple) examples of when the MAP and ML estimators would be the same? What are the advantages of Light Application objects I was hoping that the introduction of "Light Application object" would do something about the data storage of junction objects, but it doesn't seem to do anything about it.  The  seems limited to why I would use a "Light Application object", what are the advantages? Make an object invisible to a specific camera? (Cycles) Python analog of PHP's natsort function (sort a list using a "natural order" algorithm) (weak) homotopy equivalence Noticing that Newtonian gravity and electrostatics are equivalent, is there also a relationship between the general relativity and electrodynamics? I have a function with the same name, but with different signature in a base and derived classes. When I am trying to use the base class's function in another class that inherits from the derived, I receive an error. See the following code:  class A {     public:     void foo(string s){}; };  class B : public A {     public:     int foo(int i){}; };  class C : public B {     public:     void bar()     {         string s;         foo(s);     } };   I receive the following error from the gcc compiler:  In member function `void C::bar()': no matching function for call to `C::foo(std::string&amp;)' candidates are: int B::foo(int)   If I remove int foo(int i){}; from class B, or if I rename it from foo1, everything works fine.   What's the problem with this? Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$ I want to evaluate the following integral via complex analysis $$\int\limits_{x=0}^{x=\infty}e^{-ax}\cos (bx)\operatorname d\!x \ \ ,\ \ a &gt;0$$  Which function/ contour should I consider ? Do free falling observers see gravitational blueshift? Observers at rest in gravitational fields will see infalling light signals as blueshifted.  Do inertial observers in free fall in a gravitational field see the same shift?  If someone is standing on a cliff at rest in the gravitational field and then steps off, do they instantly see a change in the blueshift as a result of being in free fall in an inertial reference frame?