What is the $B^{-1}$ if $B^2 -5B + I = 0$ I think how I did it was that I did $B (B -5I) = -I$ and then divided both sides by $-1$ to get $B (-B+5BI) = I$ and then said $(-B+5I) = B^{-1}$.   Is this correct or is there a better way of doing it/answer?
Proving Invertibility and Eigenvalues If matrix $A$ is an $n\times n$ matrix such that $A^2 -A -2I=0$.  How can I show that $A$ is invertible and that $A^{-1} = \frac12(A-I)$? Also, how do I show that one of the eigenvalues of $A$ is $2$ or $ -1$? I appreciate any help on this question.
Maximum and Minimum values for ints How to implement Enums in Ruby? How Do I Allow A Standard User to Install Programs? Yes, I realize that defeats the purpose of standard user. But here is the situation. A friend of mine wants to set up time limits for his home schooled son, and his son needs to be a standard user in order to use Family Safety. But at the same time, his son (who I personally think is way too old to have time limits), needs to be able to update and install some of his games on his computer. So I guess it's just sort of "light" parental control (just something to help him focus and not get distracted with hours of gaming).  It is the basic version of Windows 8.1, so there is no Group Policy editor (gpedit.msc). However, I'm fairly good with computers and I figured out how to install it. But it doesn't have a lot of the features that the "real" gpedit seems to have. Here is an example of what is in my gpedit: Notation: Why write the differential first? Confused! Are there any differences between "I have to go", "I had to go", "I've had to go", "I get to go", "I got to go", "I've got to go"? I am Confused!   Are there any differences between "I have to go", "I had to go", "I've had to go", "I get to go", "I got to go", "I've got to go"?  In which situation is each term used?  I checked this dictionary , &amp; found that      get to do something:  to have the opportunity to do something   Seem like if you have a opportunity to do something, then use "get".  The expression is in present but why we use present perfect tense (Ex: I've got to go) here? Do we really need a [source-code] tag? The  tag doesn't appear to be very useful.  It's used in a variety of ways (for reading, writing, showing, transforming, compiling, translating, obfuscating, obtaining, ... source code) on 1747 questions right now, and doesn't appear to be adding any classification value to the site.  Can we get rid of it? If I open up many tabs in Chrome, the Tabs start to shrink. This is usually a normal behavior if the tabs would use the whole availible space, BUT in my case the tabs shrink too much. They don't use up the whole availible space anymore, but only go until somwhere at three quarters of the window. The more tabs I open, the larger the availible space gets until it reaches a maximum. This strikes me as somewhat not so normal.  Another funny thing is, if I use a second Monitor to extend my Desktop, Tabs will be smaller on the second Desktop and will only fill half the availible space from the beginning. For example right now I have 6 tabs open, which fill out approximately half the availible space. If I open more tabs, only the tab size reduces. This has not been like that when I first installed the browser.  This is what it looks like:    Is there any solution for this?   I hereby explicitly mean NO extensions. I found enough extensions to handle tabs. I just want them to behave normally without any of those tab-extensions. Re-Installing Chrome does NOT work, I tried that. Conformal transformation/ Weyl scaling are they two different things? Confused! I am working on a proof about Dedekind cuts on the positive rational numbers. I have been stuck for a while on the following point and would appreciate any help.  Given $x\in \mathbb{Q}^+$ such that $x^2&lt;2$, how to find $y\in \mathbb{Q}^+$ such $y&gt;x$ and $y^2&lt;2$? 4 fast cores or 6 slower ones? Small Caps and Bold Face I can't seem to have both the small caps and boldface styles on a line:  \huge\sc\bf Hello   This will generate bold text, and if the \sc is placed after, it will generate small caps text but not bolded. They seem to override each other, so is there any way to apply them both? Is a set without limit points necessarily closed? According to the definition on Rudin' Principles of Mathematicial Analysis, closed set is defined as:      $E$ is closed if every limit point of $E$ is a point of $E$.   Then I have a question: if a set has no limit point, is it necessarily closed? I think this idea doesn't contradict the definition of closed sets. Am I right?  And another question is #10 in Chap.2 of Rudin's:      Let $X$ be an infinite set. For $p\in X$ and $q\in X$, define    $d(p,q)=0$ when $p=q$. Otherwises,$d(p,q)=1$.    I have known that every set in the metric space is closed. To prove it, we can show that the complement of any set is open, which is quite trivial. My question is: how can we prove that every set is closed just by checking according to the definition of closed set, i.e. how can we show that every limit point of any arbitrary set $E$ in the metric space is a point of $E$?   Thanks in advanced! Comparing negatives: "she seems not to know" vs. "she doesn't seem to know" What is the difference in style and meaning between the following two:        She seems not to know.   She doesn't seem to know.      Is there a name to this type of construction? Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$. How to use wc and piping to find how many files and directories are in a certain directory? How can I use word counter (wc) and piping to count how many files or directories are in the /usr/bin directory? Pdf bookmark error in beamer Hi. I've compiled a Persian language beamer file by both luapersian and persian babel package using LuaLaTex, and in both I've the same problem in pdf bookmark as shown in the figure (some strange characters are shown instead of correct characters). Can't get my model out of wireframe mode I'm new to Blender and this site, so I apologize in advance if I'm not following any of the proper etiquette.  I'm no artist, but I'm trying to learn Blender so that I have some programmer art for me to work around in Unity.    I followed a tutorial for making a basic human model, I rigged it with rigify, and now I'm starting to export it following yet another tutorial.  The thing is, when I was trying to rig the model, I couldn't get the model to go transparent so that I could see the bones inside the model.  Eventually, I managed to get it into wireframe mode, but I can't get it back into solid mode.    It's probably just a display thing and not a property of the model itself, but I want to be sure.  I'm looking at the display options under the "Figure" pane in Blender, and none of the Display check boxes are checked, including the one that says "Wire".  I don't want to import a plain wireframe model into Unity, and even if that doesn't happen, this is functionality of Blender that I should really know anyway, so I'd appreciate any help that anyone has to offer.  If necessary, I can upload the .blend file, but I'm not sure what site people would prefer that I upload it to. "Not being good at swimming, he didn't like it." Could we omit the word "being" here? Not being good at swimming, he didn't like it.   Could we omit the word "being" here?     Not good at swimming, he didn't like it.   Which one is grammatically correct? Evaluate $\lim_{y\to 0} \dfrac {(x+y)\sec (x+y) - x\sec x}{y}$ Evaluate $\lim_{y\to 0} \dfrac {(x+y)\sec (x+y) - x\sec x}{y}$.  My Attempt: $$=\lim_{y\to 0} \dfrac {(x+y) \sec (x+y) - x\sec x}{y}$$ $$=\lim_{y\to 0} \dfrac {x\sec (x+y) + y\sec (x+y) - x\sec x}{y}$$ $$=\lim_{y\to 0} \dfrac {x(\sec (x+y) - \sec x) + y\sec (x+y)}{y}$$ Is it possible to animate which characters of a text object are assigned to a material?