Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 13

Equality of an Inequality

I encountered the following problem in my textbook-Let $a, b, c$ be three arbitrary real numbers. Denote $$ x = sqrt{b^2-bc+c^2}, y = sqrt{c^2-ca+a^2}, z = sqrt{a^2-ab+b^2} $$...

Asked on 01/01/2022

1 answer

Efficient Method to Find A Root and/or Minima of A Multivariate Polynomial With Constraints on the Variables

I have a polynomial $P(x,y,z,...)$ which has integer coefficients and real roots. I want an efficient method that is guaranteed to find a root (I only need one), and...

Asked on 01/01/2022

0 answer

For what values of $k$ is the following matrix diagonalizable?

The matrix is:$$begin{bmatrix}k&1\0&k^2end{bmatrix}$$I am aware that a square matrix is diagonalizable if there exists a matrix $P$ such that $D = P^{-1 }* A * P$...

Asked on 01/01/2022 by Math Comorbidity

1 answer

Rearrangement of matrix inverse sum expression

I have an expression of the below form: $$sum_{i=1}^k (A_i+B)^{-1}=0$$where ${A_i}_{iin {1,...k}}$ are a set of known square symmetric invertible matrices and $B$ is an unknown...

Asked on 01/01/2022

0 answer

If $F, K$ are fields, $F$ algebraically closed, and $F subseteq K$ then $K = F$?

I want to show that an algebraically closed field $F$ cannot be contained in a larger field $K$. So if $F subseteq K$ then $F =...

Asked on 01/01/2022

1 answer

Difference in eigenvalue equations

I came across a strange equation in the solution to a problem. It looks like this:$$My - Mx = lambda x$$ In this problem $M$ is an ...

Asked on 01/01/2022

2 answer

Existence of limit for sequence $x_n=frac12left(x_{n-1}+frac8{x_{n-2}}right)$ with initial values $x_0=5,x_1=10$

Let $x_0=5,x_1=10,$ and for all integers $nge2$ let $x_n=frac12left(x_{n-1}+frac8{x_{n-2}}right).$ By induction, we have $forall minmathbb Z_{ge0}enspace x_m>0,$ so we can avoid division by $0$ and...

Asked on 12/29/2021 by xFioraMstr18

3 answer

Calculate the total possible number of combinations out of x permutations, that's would sum to the same value.

Is it possible to calculate the total number of combinations that sum to a given value from x permutations? For example, a 4 digit combination has 10,000 permutations from 0000...

Asked on 12/29/2021 by NRApps

1 answer

Property of Lebesgue measure in $mathbb{R}^2$

Let $I=[0,1]times [0,1]$ and $Esubset mathbb{R}^2,$ be a set of zero Lebesgue measure. Is it true that $$overline{Isetminus E}=I?$$ I guess that the counterexample will be some...

Asked on 12/29/2021

2 answer

Trouble on Factorizing

I have trouble factoring $ a^2+ab+b^2 $.It can be done easily using $omega$, which is a complex cube root of unity with non-zero imaginary part-$$...

Asked on 12/29/2021

1 answer

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