Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 180

Find the determinant of a matrix $A$, such that $A^4 + 2A = 0$

Find the determinant of an revertible, $6 times 6$ matrix $A$, such that $A^4 + 2A = 0$This question seems odd to me, because when I...

Asked on 12/10/2020 by avivgood2

2 answer

Question about the correspondece between unitary Mobius transformations and quaternions.

One of the main theorems about the classification of Mobius transformations states that pure rotations of the Riemann sphere (without translation and dilatation) correspond to unitary Mobius transformation; that is,...

Asked on 12/10/2020 by user2554

0 answer

How do we show $P(A) leq P(A Delta B) + P(A cap B) leq P(ADelta B) + P(B).$?

In some questions I have been going through here, I came across this inequality several times. $A$ and $B$ are RV. How do we show$$P(A) leq...

Asked on 12/10/2020 by user825841

1 answer

Prove that $H<GRightarrow |H|le leftlfloor frac{|G|}{2}rightrfloor$ without Lagrange's theorem.

Suppose we do not have yet the notion of coset, and thence Lagrange's theorem either. So, if $G$ is a finite group and $H<G$, we just know that...

Asked on 12/10/2020

1 answer

Cauchy-Schwartz Inequality problem

Let $a,$ $b,$ $c,$ $d,$ $e,$ $f$ be nonnegative real numbers. (a) Prove that$$(a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) ge...

Asked on 12/10/2020 by In-finite

2 answer

Solving the Diophantine equation $x^2 +2ax - y^2 = b$ in relation to Integer Factoring

Is there a method we could use for solving the Diophantine equation $x^2 +2ax - y^2 = b$? Background: Consider a very large integer $z$ that we want...

Asked on 12/10/2020 by vvg

0 answer

Subgroup element composition

Please validate the following proof.Let $H$ be a subgroup of the Abelian group $G$ with elements $h in H$ and $g in G$ but ...

Asked on 12/10/2020 by conchild

3 answer

Motivation of Jacobi symbol

I fancy the motivation of introducing Legendre symbol is to simplify the quadratic residue check. But, for Jacobi symbol, even when its value is...

Asked on 12/09/2020 by athos

0 answer

Convergence of points under the Mandelbrot iterated equation

I was looking at $z_n=z_n^2+z_0$ and I realized I didn't know what convergence actually looked like, even in real numbers. I picked a really easy number, -0.5, to...

Asked on 12/09/2020 by Robert Kaman

1 answer

Finding the quadrilateral with a fixed side and perimeter that has a maximum area

Given a quadrilateral ABCD with a fixed perimeter and the side AD having a fixed lengthhow can we prove that quadrilateral with maximum area satisfying the conditions above must...

Asked on 12/09/2020 by Ak2399

1 answer

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