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This is a very broad question apparently, but is there any systematic way to obtain (sort of) sharp estimates for roots of complicated equations? Or maybe bounds for the roots?...
Asked on 01/09/2021 by Landon Carter
3 answerHow many solutions does the equation $x_1+x_2+x_3+x_4=1$ have? $x_i$ are integers between $-3$ and $3$. Hints please!...
Asked on 01/09/2021 by Socket1814
1 answerLet $u$ and $v$ be $2$ non-zero (column) vectors in $mathbb R^n$. Let $A = I- uv^T$ where $I$ is the $n times...
Asked on 01/09/2021 by JOJO
0 answerHere is the problem I am working on:If $M$ is a finitely generated torsion module over a PID $R$ such that there exists $m in M$ with...
Asked on 01/09/2021 by user193319
0 answerI was thinking about the formula that gives us the expected value of a continuous random variable with pdf $f(x)$, that is $$E[X]=int_{a}^{b} xf(x)dx$$How can this, intuitively,...
Asked on 01/09/2021 by thenac
1 answerProve that the set $mathbb{Q}left[sqrt2right] = left{a + b sqrt2 : a, b in mathbb{Q}right}$ is an $mathbb{Q}$-vector spaceI'm so confused with this exercise. I know $mathbb{Q}$...
Asked on 01/09/2021 by Robertoherb
3 answer$$ L(u)=u_{xx}+u_{yy}quad 0<x,y<1$$with homogenous boundary conditions. I have tried finite difference method,$$ u_{xx}=frac{u_{i-1,j}-2u{i,j}+u_{i+1,j}}{h^2}$$$$ u_{yy}=frac{u_{i,j-1}-2u{i,j}+u_{i,j+1}}{h^2}$$Substituting in our equation, we have$$ (u_{i-1,j}-2u{i,j}+u_{i+1,j})+(u_{i,j-1}-2u{i,j}+u_{i,j+1})=0$$after...
Asked on 01/08/2021 by Momo
1 answerI need help with this question: A bag contains $2$ red balls, $6$ blue balls and $7$ green balls. Victoria draws $2$ balls out ofthe...
Asked on 01/08/2021 by Ryan Soh
2 answerSuppose $mathbf{u},mathbf{v},mathbf{w}$ are noncollinear points $inmathbb{R}^2$. Let $mathbf{x} in mathbb{R}^2$. Show that we can write $mathbf{x}$ uniquely in the form $mathbf{x} = rmathbf{u}+smathbf{v}+tmathbf{w}$ where ...
Asked on 01/08/2021
2 answerI'm trying to show that the commutator subgroup $[F_2,F_2]$ is not a retract of $F_2$. I was trying to do the proof by contradiction so I assume...
Asked on 01/08/2021 by Sasha
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