Updates - Velvet Chronicle

Category: Updates

What is the representation matrix of this operator?

Emma Horne Apr 09, 2026

To determine the eigenvalues of $L$ I need a representation matrix of: $$L: \mathbb{R} [X]_p \to \mathbb{R} [X]_p,\quad f \mapsto [(1-X^2)f']' $...

$Show that $\frac{ax+b}{cx+d}:=z$ is irrational with $a,b,c,d,x \in \mathbb{R} ,x$ irrational and $ad\neq bc ,cx+d \neq 0$ and $a,b,c,d$ rational$

Show that $\frac{ax+b}{cx+d}:=z$ is irrational with $a,b,c,d,x \in \mathbb{R} ,x$ irrational and $ad\neq bc ,cx+d \neq 0$ and $a,b,c,d$ rational

Daniel Cobb Apr 09, 2026

I know that $ad\neq bc $ is sufficient for $z$ irrational because if $ad = bc$ then $\frac{ax+b}{cx+d} = \frac{ax+b}{cx+d} \frac{cb}{ad} = \frac{cax+cb}{c...

Find all vectors orthogonal to two parallel vectors

Daniel Cobb Apr 09, 2026

Find all vectors $\vec{v}=\begin{bmatrix}x\\y\\z\end{bmatrix}$ orthogonal to both $\vec{u_1}=\begin{bmatrix}2\\0\\-1\end{bmatrix}$ and $\vec{u_2}=\begin{b...

finding a vector field when given curl(F)

William Jenkins Apr 09, 2026

Is there a vector field F such that Curl(F) = ($xy^2$, $yz^2$, $zx^2$)? Explain. Ive been testing it out myself, coordinate by coordinate, and once determ...

Sum of Squares $i^2$

John Hall Apr 09, 2026

I want to show that the sum of integer squares from $i=1$ to $n$ is $\frac{n(n+1)(2n+1)}{6}$ I've watched some videos and read other posts about it b...

$Determining the order of convergence of $ X_{n+1} = \frac{(X^3_n + 3aX_n)}{(3X^2_n + \alpha)} $$

Determining the order of convergence of $ X_{n+1} = \frac{(X^3_n + 3aX_n)}{(3X^2_n + \alpha)} $

Emma Horne Apr 09, 2026

I need to find the order of convergence for: $$ X_{n+1} = \frac{(X^3_n + 3aX_n)}{(3X^2_n + \alpha)} $$ In a previous part we are told $\alpha$ = 2 and $x_...

$What is the difference between ($\tan x \sec^2x$) and ($\sin x/\cos^3x$)? Why is the answer to the integration different?$

What is the difference between ($\tan x \sec^2x$) and ($\sin x/\cos^3x$)? Why is the answer to the integration different?

Emma Horne Apr 09, 2026

$$\int \:\frac{\left(\sin x+\tan x\right)}{3\cos^2x}dx$$ I know I have to split the equation into $$\frac{1}{3}\int \:\left(\:\frac{\sin x}{\cos x}\right)...