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Mathematics : Recent Questions and Answers

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Suppose $A , B , C$ are arbitrary sets and we know that $( A times B ) cap ( C times D ) = emptyset$ What conclusion can we draw?

$( 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

3 answer

Can a nonsingular matrix be column-permuted so that the diagonal blocks are nonsingular?

Suppose 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

1 answer

Does ${f(x)=ln(e^{x^2})}$ reduce to ${x^2ln(e)}$ or ${2xln(e)}$?

I'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

3 answer

Proving that $(0,1)$ is uncountable

I 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

2 answer

Understanding a statement about composite linear maps

I 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

1 answer

Assert the range of a binomial coefficient divided by power of a number

I 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

3 answer

What is the Fourier transform of $|x|$?

I 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 answer

Exists $t^*in mathbb{R}$ such that $y(t^*)=-1$?.

$y'=y^2-13y+77, y(0) = frac{13}{2}$ 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

2 answer

Proving $logleft(frac{4^n}{sqrt{2n+1}{2nchoose n+m}}right)geq frac{m^2}{n}$

I 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

2 answer

Linearized system for $ begin{cases} frac{d}{dt} x_1 = -x_1 + x_2 \ frac{d}{dt} x_2 = x_1 - x_2^3 end{cases} $ is not resting at rest point?

Assume 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

1 answer

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