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$( A cap C ) times ( B cap D ) = emptyset$$B cap D = emptyset$$A cap C = emptyset$$A cap D = emptyset$I feel...

Asked on 11/29/2021 by Anonymous Molecule

3Suppose that $Ain M_{n+m}(mathbf C)$ (i.e. a $(n+m)times (n+m)$ complex matrix) is non-singular. Is it always possible to find a permutation matrix $P$ so that ...

Asked on 11/29/2021 by syeh_106

1I'm confused with the expression ${f(x) = ln(e^{x^2})}$.I know the rule ${log_a(x^p) = plog_a(x)}$. So does the given expression reduce to ${x^2ln(e)}$ or ${2xln(e)}$?...

Asked on 11/29/2021 by EVO

3I have this proof: "Suppose by contradiction that $(0, 1)$ is countable. This means we can find asequence $(x_n)$ such that for every $x ∈ (0,...

Asked on 11/29/2021 by Henry Brown

2I know the definition of a bijective linear map $L: V rightarrow W$ (one that is both injective and surjective). However, my book states that it is equivalent to...

Asked on 11/29/2021

1I found this question in a previous year post graduate entrance exam for mathematics.The question was What is the range ofbegin{equation*}frac{200 choose 100}{4^{100}}end{equation*} The choices...

Asked on 11/29/2021 by vib_29

3I am trying to find the Fourier transform of $|x|$ in the sense of distributions in its simplest form. Here is what I have done so far: Let...

Asked on 11/29/2021

3$y'=y^2-13y+77, y(0) = frac{13}{2}$ Exists $t^*in mathbb{R}$ such that $y(t^*)=-1$?. How to prove without solving the ode? Any hint? Using previous post: We have: $y^2-13y+77=0...

Asked on 11/29/2021 by user514695

2I have tried doing this exercise, Let $m,ninmathbb{N}, mleq n$, prove that$$logleft(frac{4^n}{displaystylesqrt{2n+1}{2nchoose n+m}}right)geq frac{m^2}{n}$$ I achieved some results like for example,$$displaystylesum_{i=0}^n 2^ibinom{2n-i}{n} = 4^n$$ and...

Asked on 11/29/2021 by Zaragosa

2Assume there is the dynamical system $$begin{align}frac{d}{dt} x_1 &= -x_1 + x_2 \frac{d}{dt} x_2 &= x_1 - x_2^3end{align}$$ The system is at rest...

Asked on 11/29/2021 by user3137490

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