If Ax = 0 for every x in $R^n$, A is a zero matrix
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
I am new to Stack Exchange. I know there is a lot of discussion sites for Stack Exchange. I would like to know about there were any Stack Exchange site available for discussing and solving personal psychological problems. How do I update Custom Label's value using apex? Which one would be a better option metadata api or tooling api? Please provide example I'am working on post deployment automation process in salesforce. I am stuck on how should I update values in custom labels which needs tobe updated manually after a sandbox refresh. Which way is up? (electric outlet) My house has electric outlets in both orientations.  Which one is correct?  Should the ground hole be at the bottom or the top?    OR Why does a helium filled balloon move forward in a car when the car is accelerating? Not sure if the title is specific enough, so here we go:  I crashed my Windows pc, and now I want to install Ubuntu on that computer. I'm currently using my Mac, as it is the only operable computer I have left. I have downloaded the .iso. I guess my question is; How do I go about installing Ubuntu on my crashed computer from the external harddrive? I've used Ubuntu before, but I used to install it from a CD-rom. I tried reading the instructions, but couldn't really understand them. Please help  Edit: As Tom mentioned, I only want to install Ubuntu on the (formerly) Windows machine.  Anyways, thanks for the quick responses, I think I've got it from here. Cheers Is there a reason, beyond historical reasons, that three phases has become the dominant number of phases?  I am aware of the advantages against one phase and two phase, namely the reduced amount of conductor needed, and that motors can provide torque when stalled (and less pulsation).  Is this solely due to diminishing returns, with only a small increase in smoothness of torque application, at the cost of increased complexity (increased number of wires (albeit of smaller CSA)).  To be clear, the phases are all evenly distributed, that is, five phases separated by 72 degrees. Fail of markdown parser detected if '_ 's are used in a naked URL In the answer , the parser breaks my URL link.  The URL was with __word__:      http://www.open-mpi.de/projects/hwloc/doc/v1.2/group__hwlocality__membinding.php#gade5e2c28ea8475a479bf2b1df36c6ccd   After parsing, it becomes (&lt;a href is broken; no clickable link):  hwlocality_membinding.php#gade5e2c28ea8475a479bf2b1df36c6ccd"&gt;http://www.open-mpi.de/projects/hwloc/doc/v1.2/group_hwlocality_membinding.php#gade5e2c28ea8475a479bf2b1df36c6ccd   Short test:  http://example.com/_test_ -> test"&gt;http://example.com/test  Or if I put in a naked URL with _test_ just here: What will reduce my rendertime? What would reduce the render time? Should I get a better GPU or more RAM? I'd really value your thoughts on this one. I'm familiar with the following use of 'made of':  The shirt is made of silk.  But I'd like to know if anyone thinks using this phrasal verb as a synonym for comprise/consist of/be composed of/made up of is actually grammatically correct/non-standard usage.  The board is made of five members. The board is made up of five members.  A few instances of this usage came up on a google search, but I'm not convinced... $ f:\mathbb C\rightarrow \mathbb C$ defined by $f(z)=0$, if $Re(z)=0$ or $Im(z)=0$ and $f(z)=z$, otherwise. Going to any question on the site brings an error page How to solve ~(P → Q) : P & ~Q by natural deduction? I'm trying to solve the following by natural deduction:  ~(P → Q) : P &amp; ~Q  It's a trivial problem if identities are used, as can be seen by the following:   {1}      1.   ~(P → Q)                    Prem. {1}      2.   ~(~P ∨ Q)                   1 Mat. Impl. {1}      3.   ~~P & ~Q                    2 De Morgan's {1}      4.   P & ~Q                      3 DNE   Starting from step 2 of the previous proof, it's also fairly straightforward to reach a conclusion using natural deduction; i.e. starting from ~(~P ∨ Q), which is an identity of ~(P → Q):  ~(~P ∨ Q) :  P &amp; ~Q   {1}      1.   ~(~P ∨ Q)                   Prem. {2}      2.   ~P                          Assum. {2}      3.   ~P ∨ Q                      2 ∨I {1,2}    4.   ~(~P ∨ Q) & (~P ∨ Q)        1,3 &I {1}      5.   P                           2,4 RAA {6}      6.   Q                           Assum. {6}      7.   ~P ∨ Q                      6 ∨I {1,6}    8.   ~(~P ∨ Q) & (~P ∨ Q)        1,7 &I {1}      9.   ~Q                          6,8 RAA {1}      10.  P & ~Q                      5,9 &I   I also found that it's fairly easy to conclude ~Q:   {1}      1.   ~(P → Q)                    Prem. {2}      2.   Q                           Assum. {3}      3.   P                           Assum. {2,3}    4.   P & Q                       2,3 &I {2,3}    5.   Q                           4 &E {2}      6.   P → Q                       3,5 CP {1,2}    7.   ~(P → Q) & (P → Q)          1,6 &I {1}      8.   ~Q                          2,7 RAA ... {1,2}    12.  P & ~Q   In spite of how easy it looks, I can't figure out how to do it. I believe it can be done in 12 steps. Thanks! Why do mirrorless cameras have quicker autofocus than SLRs using live view? Problem using atan in pgfplots how to get line spacing greater than one and half spacing and less than double space Does anyone know how to get line spacing in a paragraph to be greater than one and half spacing and less than double spacing? I tried \renewcommand{\baselinestretch}{value} but it did not work. What is likely to happen when you plug two ends of a network cable to a single switch/router? Will this create problems on the network, or just be ignored? How do I get the form id of my form? I've just begun to make my modules and I'm at a standstill. I got this code from someone else and am trying to customize it:  function hook_form_alter(&amp;$form, &amp;$form_state, $form_id) {   if ($form_id == 'the form id for the node form') {     $form['#submit'][] = 'my_custom_submit_handler';   } } How can I 'join' an array adding to the beginning of the resulting string the first character to join? Fantasy book series with non-human races and labyrinth I'm trying to identify fantasy book series I encountered some time ago. Here are things I remember:   it was a fantasy setting but with some s-f elements; with many worlds and possibility to travel between them; resembling  setting a little, the two main races were non-human and probably hostile to each other,  a labyrinth (?), which somehow played an important role in the plot, a protagonist was some kind of emissary and was sent on a mission to another worlds  time period: 80s - 90s    Does anyone know what it is the name of the series? Possible to replay repetitive tasks using Python?