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  • Is thi set of vectors, $\ { (2, 1), (3, 2), (1, 2)\}$, is linearly . . .
    Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,
  • Given a 95% confidence interval why are we using 1. 96 and not 1. 64?
    The Z-score for 90% is -1 6444 and 1 6444 , 1 sigma The z-score for 95% is -1 96 and 1 96 , 2 sigma The z-score for 99% is -2 5758 and 2 5758 , 3 sigma in your Estimation of Population Mean meaning, that mean plus or minus 1 96 times its standard deviation gives 95% C I Errors distr estimation is considered to use t-distr with fatter tails than Normal distr , but with increasing size of
  • What does versus mean in the context of a graph?
    I would agree with the rule " [dependent] versus [independent] " The word "versus" can mean "compared with," and it more frequently makes sense to compare a dependent value with its associated independent value, because well, the independent variable doesn't really "care" about the existence of the dependent variable, but the converse relationship is by definition
  • How do the definitions of irreducible and prime elements differ?
    You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
  • What does open set mean in the concept of a topology?
    Often a course in topology starts with metric spaces Then a definition of "open set" arises in that context It can be shown that the collection of these sets has the properties mentioned in def 2 2 and for such a collection a name allready exists: a topology That opens the door to reach out for a more general definition of open set wich is not linked only with metric spaces, but with
  • Difference between $⊂$ and $⊆$? - Mathematics Stack Exchange
    I was solving the exercises in Discrete Mathematics and its applications book Determine whether each of these statements is true or false {0} ⊂ {0} {∅} ⊆ {∅} I thought both 1 and 2 are true,
  • linear algebra - Relation between determinant and matrix rank . . .
    It is often taken as the definition of rank of a matrix I see a proof of the "determinant rank" being the same as the "row rank" in the book Elementary Linear Algebra by Kenneth Kuttler, which I see in google books They come as Theorem 8 5 7 and Corollary 8 5 8 The proof looks pretty elementary to me
  • Explanation and proof of the 4th order Runge-Kutta method
    There are many Runge–Kutta methods The one you have described is (probably) the most popular and widely used one I am not going to show you how to derive this particular method – instead I will derive the general formula for the explicit second-order Runge–Kutta methods and you can generalise the ideas In what follows we will need the following Taylor series expansions \begin {align
  • How is that a rotation by an angle θ about the origin can be . . .
    Draw a figure with normal and rotated axes and a point (x,y) See if you can drive the new coordinates wrt the old using simple trigonometry
  • Find the value of the constant k that makes the function continuous
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