The system of equations are:  $\begin{cases}x+y+kz = 1\\x+ky+z=1\\kx+y+z=1\\ \end{cases}$  I am looking to finding values of $k$, for which this system has either no solutions, infinite many solutions or a unique solution (if any).  I've had a look around the web for some help, and know that this question has been asked, but in a way that I have not yet learnt (something to do with determinants I think).  However, I have only been working with reducing the matrix to REF/RREF and thus I'm trying to find rows, such as $( 0 \ 0 \ 0 \mid 2)$ and $( 0 \ 0 \ 0 \mid 0)$ etc to show if we have no solutions or infinite many solutions, for instance.  So far, I've got the following:  $\left[\begin{array}{ccc|c}1&amp;1&amp;k&amp;1\\1&amp;k&amp;1&amp;1\\k&amp;1&amp;1&amp;1\end{array}\right]$  Then, $R_2$$\mapsto$$R_2-R_1$  $\left[\begin{array}{ccc|c}1&amp;1&amp;k&amp;1\\0&amp;k-1&amp;1-k&amp;0\\k&amp;1&amp;1&amp;1\end{array}\right]$  Then, $R_2$ $\leftrightarrow$ $R_3$   $\left[\begin{array}{ccc|c}1&amp;1&amp;k&amp;1\\k&amp;1&amp;1&amp;1\\0&amp;k-1&amp;1-k&amp;0\end{array}\right]$  This is where I got stuck, and I'm not sure how to continue.  Thank you in advance, and I'm sorry if this question has been asked and solved in the same way as presented above.  Cheers.
For which real values of t does the following system of linear equations:  $$ \left\{  \begin{array}{c} tx_1 + x_2 + x_3 = 1 \\  x_1 + tx_2 + x_3 = 1 \\  x_1 + x_2 + tx_3 = 1 \end{array} \right.  $$  Have:  a) a unique solution?  b) infinitely many solutions?  c) no solutions?  I haven't done linear algebra in almost a year, so I'm really rusty and could use some pushes in the right direction.
SQL Server Escape an Underscore How do I escape the underscore character?  I am writing something like the following where clause and want to be able to find actual entries with _d at the end.  Where Username Like '%_d' What's a way to implement a flexible buff/debuff system? Overview:  Lots of games with RPG-like statistics allow for character "buffs", ranging from simple "Deal 25% extra damage" to more complicated things like "Deal 15 damage back to attackers when hit."  The specifics of each type of buff aren't really relevant.  I'm looking for a (presumably object-oriented) way to handle arbitrary buffs.  Details:  In my particular case, I have multiple characters in a turn-based battle environment, so I envisioned buffs being tied to events like "OnTurnStart", "OnReceiveDamage", etc.  Perhaps each buff is a subclass of a main Buff abstract class, where only the relevant events are overloaded.  Then each character could have a vector of buffs currently applied.  Does this solution make sense?  I can certainly see dozens of event types being necessary, it feels like making a new subclass for each buff is overkill, and it doesn't seem to allow for any buff "interactions".  That is, if I wanted to implement a cap on damage boosts so that even if you had 10 different buffs which all give 25% extra damage, you only do 100% extra instead of 250% extra.  And there's more complicated situations that ideally I could control.  I'm sure everyone can come up with examples of how more sophisticated buffs can potentially interact with each other in a way that as a game developer I may not want.  As a relatively inexperienced C++ programmer (I generally have used C in embedded systems), I feel like my solution is simplistic and probably doesn't take full advantage of the object-oriented language.  Thoughts?  Has anyone here designed a fairly robust buff system before?  Edit: Regarding Answer(s):  I selected an answer primarily based on good detail and a solid answer to the question I asked, but reading the responses gave me some more insight.  Perhaps unsurprisingly, the different systems or tweaked systems seem to apply better to certain situations.  What system works best for my game will depend on the types, variance, and number of buffs I intend to be able to apply.  For a game like Diablo 3 (mentioned below), where nearly any bit of equipment can change a buff's strength, the buffs are just character stats system seems like a good idea whenever possible.  For the turn-based situation I'm in, the event-based approach may be more suitable.  In any case, I'm still hoping someone comes along with a fancy "OO" magic bullet which will allow for me to apply a +2 move distance per turn buff, a deal 50% of damage taken back to the attacker buff, and a automatically teleport to a nearby tile when attacked from 3 or more tiles away buff in a single system without turning a +5 strength buff into its own subclass.  I think the closest thing is the answer I marked, but the floor is still open.  Thanks to everyone for the input. Ubuntu 13.10 to 14.04 Lts does not upgrade, keeps showing error The update from Ubuntu 13.10 to 14.04 LTS does not work it keeps showing me an error as could not calculate the upgrade, even when I want it to get updated from the terminal it says the same error. I did not use the beta its the final Ubuntu 14.04 LTS.I have restarted my laptop for like 5-10 times no change. Disabling the software sources also does not help. What techniques are available for collapsing (or pooling) many categories to a few, for the purpose of using them as an input (predictor) in a statistical model?    Consider a variable like  (discipline chosen by an undergraduate student). It is unordered and categorical, but it can potentially have dozens of distinct levels. Let's say I want to use major as a predictor in a regression model.  Using these levels as-is for modeling leads to all sorts of issues because there are just so many. A lot of statistical precision would be thrown away to use them, and the results are hard to interpret. We're rarely interested in specific majors -- we're much more likely to be interested in broad categories (subgroups) of majors. But it isn't always clear how to divide up the levels into such higher-level categories, or even how many higher-level categories to use.  For typical data I would be happy to use factor analysis, matrix factorization, or a discrete latent modeling technique. But majors are mutually exclusive categories, so I'm hesitant to exploit their covariance for anything.  Furthermore I don't care about the major categories on their own. I care about producing higher-level categories that are coherent with respect to my regression outcome. In the binary outcome case, that suggests to me something like linear discriminant analysis (LDA) to generate higher-level categories that maximize discriminative performance. But LDA is a limited technique and that feels like dirty data dredging to me. Moreover any continuous solution will be hard to interpret.  Meanwhile something based on covariances, like multiple correspondence analysis (MCA), seems suspect to me in this case because of the inherent dependence among mutually exclusive dummy variables -- they're better suited for studying multiple categorical variables, rather than multiple categories of the same variable.  edit: to be clear, this is about collapsing categories (not selecting them), and the categories are predictors or independent variables. In hindsight, this problem seems like an appropriate time to "regularize 'em all and let God sort 'em out". Glad to see this question is interesting to so many people! Where can questions about our community-run moderation tools be asked? The question  was recently closed due to not being "about the software that powers the Stack Exchange network, within the scope defined in the help center." MEE is Johann Gambolputty made a comment that     SmokeDetector is a community run project to help to fight spam. Therefore your question is unfortunately off-topic for this site. You can find help in  chatroom.   If questions about community run moderation bots (e.g. SmokeDetector, FireAlarm, Natty, Queen, etc.) are off-topic here on Meta Stack Exchange, is there anywhere on the Stack Exchange network where one can post a Question and Answer-style question on them, or are they only on-topic in appropriate chat rooms? Why does `htop` show more process than `ps` In ps xf  26395 pts/78   Ss     0:00  \_ bash 27016 pts/78   Sl+    0:04  |   \_ unicorn_rails master -c config/unicorn.rb                                            27042 pts/78   Sl+    0:00  |       \_ unicorn_rails worker[0] -c config/unicorn.rb                                           In htop, it shows up like:   Why does htop show more process than ps? How quickly is the desired state of curl of the Electric Field around a point achieved where a Magnetic Field Vector has just begun changing? My question and context with explanation are given below. Thank you in advance.   Faraday’s Law () states that a time-changing magnetic field vector induces a curl of the Electric field around that point. However it does not specify how quickly the necessary spatial gradient is developed in the Electric Field to satisfy that curl. Of course, the Electric Field vectors around that point cannot just jump to the required values instantaneously in accompaniment as soon as the magnetic field starts changing at a fixed rate, since it is required that the Electric Field has a sensible rate of change to in turn induce a curl of the magnetic Field and continue the propagation of the wave. It would seem the exact rates at which the Electric and Magnetic Fields are changing is critical in the mechanism of an EM wave’s propagation. How would I then calculate the rate of change of E somewhere along the wave given I know the rate of change of the B vector that began it, and given the wave is restricted to one dimension for simplicity? There should after all be some delay in how the EM wave moves from point to point in space, seeing as it moves at the finite speed of causality (3*10^8 m/s), as shown in the first image:    Some of my ideas so far have been that perhaps the rate of change of E is determined such that it exactly cancels the growth of the time-changing E vector that gave rise to a curl of B before, which developed at such a rate to induce a curl of E, which demands this rate of change of E which I am talking about now. In this way the wave might level out the growth of the fields in its wake and spread the change further outwards, in the same way smoothening out a crease spreads it elsewhere. However I am stuck on how to show this rigorously.  I am open to any difficulty of maths, so long as the answer provides the explanation. Below are some diagrams to help visualize what I am talking about:    Faraday's Law requires that a curl of E is developed, which under these restrictions requires a spatial gradient of E to appear across that point. Since the field across that point was previously in some other state, it is required that the Electric Field vectors that are infinitesimally close to that point undergo a rate of change through time to achieve the desired state of curl. The question is, how quickly is this desired state of curl achieved? primes whose difference is a multiple of $n$ Debugging scripts, what is the difference between -x to set -euxo pipefail? The main way I know to debug scripts is adding -x to the shabang (#!/bin/bash -x).  I recently came across a new way, adding set -euxo pipefail right under the shabang, as in:  #!/bin/bash set -euxo pipefail   What is the main difference between the two ways of debugging? Are there times you would prefer one above the other?  As a freshman, , I couldn't extract such conclusion. Intuitive reason why the Fisher Information of Binomial is inversely proportional to $p(1-p)$ It confuses/blows my mind that the Binomial has variance proportional to $p(1-p)$. Equivalently, the Fisher information is proportional to $\frac{1}{p(1-p)}$. What is the reason for this? Why is the Fisher Information minimized at $p=0.5$? That is, why is inference most difficult at $p=0.5$?  Context:  I'm working on a sample size calculator, and the formula for $N$, the sample size needed, is an increasing factor of $p(1-p)$, the result of a variance estimation in the derivation. Domains in cell membrane How is movement of proteins and lipids between different domains of cell membrane prevented?  Why is the noncytosolic layer not able to do lateral movements between domains but cytosolic layer is able to do so? Bizarre spacing with 4 $\star$s The spacing between the 3rd and 4th stars is non-existent. Anyone know what's up?    \documentclass[11pt]{article}  \usepackage{amsmath}  \begin{document}  \begin{gather*} \star\star\star\star \\ \star\star\star\,\star \\ \star\star\star\star\star \end{gather*}  \end{document} When I visit a site I haven't visited (while logged in) for a while, I see:  Welcome back! If you found this question useful, don't forget to vote both the question and the answers up.  That's often intended behavior. But today I visited  and was shown that banner even though the question and all its answers are locked. Voting arrows aren't even shown on any of the posts on that page. I believe that banner should be disabled on pages where there is no post that can be voted on by anyone. A man sits on a bench considering his woeful burden. He looks up at the stars and compares the distance from here to his house and here to the furthest visible star Deneb. Suddenly his problems seems pitifully faint and untroubling. He laughs and relaxes in his seat, staring at the ducks.     Look again at that dot. That's here, that's home, that's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there—on a mote of dust suspended in a sunbeam.   ~Carl Sagan      I really believe that if the political leaders of the world could see their planet from a distance of 100,000 miles their outlook could be fundamentally changed. That all-important border would be invisible, that noisy argument silenced. The tiny globe would continue to turn, serenely ignoring its subdivisions, presenting a unified façade that would cry out for unified understanding, for homogeneous treatment. The earth must become as it appears: blue and white, not capitalist or Communist; blue and white, not rich or poor; blue and white, not envious or envied. ~Michael Collins, astronaut   I'm looking for a noun or verb that describes this positive enlightening experience. During a sunny day the walls of my house warm up (no surprise). My question: how much of this warming up (if any) comes from visible light? I associate infrared with thermal energy. If my house was floating in space (to prevent any thermal exchange with its surroundings) and I installed a giant infrared (and UV) filter between it and the sun, would it still warm up (compared to its rest temperature in full darkness)? How can I remove the white pixels around the edges when exporting a transparent GIF? Rules for "on", "at", and "in": preposition of time I have been building models with categorical data for a while now and when in this situation I basically default to using scikit-learn's LabelEncoder function to transform this data prior to building a model.  I understand the difference between OHE, LabelEncoder and DictVectorizor in terms of what they are doing to the data, but what is not clear to me is when you might choose to employ one technique over another.    Are there certain algorithms or situations in which one has advantages/disadvantages with respect to the others? Can I have 8 GB RAM on 32-bit Win 7? Possible Duplicate:             According to , Win 7 only supports 4 GB of RAM. I, however have been reading some forums and some say they are using 8 GB RAM with good performance. I am wondering if I can use 8 GB before I purchase. Why is df -h size, util and dispo not corresponding to each other When I'm using the command "df -h" I'm having the following output :   Filesystem                 Size   Used  Avail Use% Mounted on /dev/mapper/fedora-root    20G    9,4G  8,8G  52% / devtmpfs                  1,9G       0  1,9G   0% /dev tmpfs                     1,9G    1,2M  1,9G   1% /dev/shm tmpfs                     1,9G    1,0M  1,9G   1% /run tmpfs                     1,9G       0  1,9G   0% /sys/fs/cgroup tmpfs                     1,9G    108K  1,9G   1% /tmp /dev/sda1                 477M    129M  319M  29% /boot /dev/mapper/fedora-home   916G    279G  591G  33% /home   Or it says my root is of 20G with 9.4 used and 8.8 still available it's 2G that disappeared. I know a very similar question as been answered here  and I'm just wondering if the reason could be the same here since I'm using LVM.  If not is there any way to reclaim that space that disappeared because for home there is an amazing 46G that disappeared.