## Winning Strategy with Addition to X=0 November 30

Problem:Two players play the following game. Initially, X=0. The players take turns adding any number between 1 and 10 (inclusive) to X. The game ends when X reaches 100. The player who reaches 100 wins. Find a winning strategy for one of the players

## Implications of zero row when row reducing matrix November 30    1

Often when I am performing elementary row operations to row reduce an arbitrary $A_{m \times n}$ matrix, a row of 0's appears, $[0 \, \, 0 \, ... \, 0\, \, 0]$.I am uncertain, does this imply either or both of the following:a row in $A$ is a linear c

## Any matrix can be reduced to a special matrix by elementary operations November 30

Definition. Let $A$ be an $r \times s$ integer valued matrix. $A$ is "special" if there exists an integer $k$ such that $a_{ij}=0$ unless $i=j$ and $i \leq k$ and $a_{ij} \neq 0$ if $i=j \leq k$.Show that any matrix $A$ can be reduced to a "

Solve the indeterminate system:a=3f$$3b=10f+9g$$3c=10f+10g+9h$$3d=10f+10g+10h+9i$$3e=10f+10g+10h+10i+9j$$3e=-jEDIT: Please don't close it, I actually want to learn. This is a challenge homework problem, not standard homework. I've tried everything ## Impossible System of Equations November 30 This is from a competition: DMM Olympiad, Ural State University P4I don't understand what the question means exactly (the first part, i.e. "exclude x or y from..." part). Does it mean "write x in terms of y or y in terms of x&qu ## Exists x, P(x) implies exists x, P(x) November 30$$\begin{align*} \exists x\,P(x)\to\exists x\,P(x) \end{align*}$$Is true? ## Grade 10 system of linear equation problem November 30 A farmer harvested 1 section (which is 640\, acres) of wheat and 2 sections of barley. The total yield of grain for both areas was 99,840\, bushels. The wheat sold for 6.35\, /bushel The barley sold for 2.70\, / bushel. The farmer receive ## Derivative with respect to y for Jacobian matrix (Newton's Method) November 30 1 I'm solving multiple equations using Newton's method. I'm working out the Jacobian matrix, and as it's late my brain is a bit hazy on partial derivatives. I have two equations:$$f_{1}:\frac{x^2}{16}+\frac{y^2}{9}=1f_{2}:y=x^x-4$$I've worked o ## Jacobian of a matrix respect to a complex vector November 30 Find the derivative of$$f(x)= \frac{1}{x_3} \begin{bmatrix} x_1 // x_2 \end{bmatrix}$$where x1, x2, x3 are the first three elements of x. ## Natural Deduction Help November 30 I desperately need help on these three natural deduction problems. If anyone can help, it'd be greatly appreciated. ## About 2-adic representation of integers November 30 How would I express -3 in 2-adic representation? Is it just revercimal calculation of binary expression of -3?like: -3 = -11 in binary, so using revercimal, -11. in binary = 01. ? ## Generalized Harmonic numbers November 30 I'd like to be able to prove the following inequality: \frac{{{H_{n, - r}}}}{{{n^r}\left( {n + 1} \right)}} \le \frac{{{H_{n - 1, - r}}}}{{n{{\left( {n - 1} \right)}^r}}}.It's clear that as n \to \infty we get equality, the limit on each side is ## Healing a frequency distribution when filling-in a group… November 30 Consider say letters in English, which follow a frequency distribution.A 8%, B 1%, C3% and so on. (eg) EF, English Frequency.Say you have to generate groups of, say, ten letters...adufaveafs grfcsriree cgrepbinii soneroeuao You want any group to foll ## Necessary theory to understand differentiable function approximation by lipschitz continuous functions November 30 In Kolmogorov & Fomin's real analysis book specifically the section on convergence, open and closed sets in metric spaces, there is the following problem, which part a) asks to proveThe set of all functions on [a,b] satisfying a Lipschitz condition ## Levy Continuity Theorem for continuous-time processes November 30 Usually, Levy Continuity Theorem is stated for sequences of random variables (i.e. \varphi_{X_n}(t)\to \varphi_X(t)\Rightarrow X_n\xrightarrow{d}X). However, can this result be extended for the case of continuous random process, i.e. we have \varp ## Probability distribution of a Poisson process November 30 Given that n events have occurred in a Poisson process N(t) with rate \lambda until the time a . Find the probability distribution of N(t) until the time b where 0<b<aMy attempt :$$P(N(a)=n)=\frac{e^{-\lambda a}(a\lambda)^n}{n!}$$We ## Necessary theory to to understand differentiable function approximation by lipschitz continuous functions November 30 In Kolmogorov & Fomin's real analysis book specifically the section on convergence, open and closed sets in metric spaces, there is the following problem, which part a) asks to proveThe set of all functions on [a,b] satisfying a Lipschitz condition ## Getting the derivative of the inverse of a function November 30 Given f(x), how would I find (f^{-1})'(x)?As an example how would I find that for this problem:f(x) = 4x^3 + 5x + 2 ## Probability distribution of a possion process November 30 Given that n events have occurred in a Poisson process N(t) with rate \lambda until the time a . Find the probability distribution of N(t) until the time b where 0<b<aMy attempt :$$P(N(a)=n)=\frac{e^{-\lambda a}(a\lambda)^n}{n!}$$We ## Find the Fourier cosine series expansion of f(x)=x,~~~ x\in (0,\pi) November 30 Find the Fourier cosine series expansion of$$f(x)=x,~~~ x\in (0,\pi)$$I went through and got the answer$$\frac{\pi}{2}+\frac{2}{\pi}\sum_{n=1}^{\infty} \frac{((-1)^n-1)cos(nx)}{n^2}$$I now need to take the derivative and am having trouble doing so You Might Also Like • Some questions about algebraic groups. Let G be an affine algebraic group over algebraically closed field ... • As I understand that there are at least two fundamental limits of the development of the mathematics:1) Goed ... • Is the following true:\sup(f+g)\ge \sup(f)+\inf (g)?If so prove it.I think its true, but I don't know how ... • how many groups can 20 (or n) people form? The size of the groups vary from 2 to 20, where no group ... • I have seen sources claim that SO^+(1,3) \cong SU(2) \times SU(2), but have seen others claim that only th ... • "Food for thought" problem in university math class. I know that symmetric matrices are diagonaliz ... • \left[\begin{pmatrix}e\\0\end{pmatrix}\right],\left[\begin{pmatrix}d\\f\end{pmatrix}\right]Sorry about the f ... • Consider the following presentation for A_4$$< p, q\, |\, p^2 = (pq)^3 = q^3 =e>$There exist eigh ... •$S^+$and$S^-$are the upper ($z\geq 0$) and lower half ($z\leq 0\$) of the surface area of a sphere with Ra ...
• Does it matter if functional analysis was introduced from a normed space versus a metric space formulation? ...