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@@ -5,57 +5,36 @@ title: "Welcome to Jekyll!"
date: 2024-07-01 12:19:36 +0200
categories: jekyll update
---
You’ll find this post in your `_posts` directory. Go ahead and edit it and re-build the site to see your changes. You can rebuild the site in many different ways, but the most common way is to run `jekyll serve`, which launches a web server and auto-regenerates your site when a file is updated.
Jekyll requires blog post files to be named according to the following format:
# Chapitre 3 : Compléments d'algèbre linéaire
`YEAR-MONTH-DAY-title.MARKUP`
## Sous-espaces vectoriels et familles de vecteurs
Where `YEAR` is a four-digit number, `MONTH` and `DAY` are both two-digit numbers, and `MARKUP` is the file extension representing the format used in the file. After that, include the necessary front matter. Take a look at the source for this post to get an idea about how it works.
## Applications linéaires
Jekyll also offers powerful support for code snippets:
### Exercice 11
{% highlight ruby %}
def print_hi(name)
puts "Hi, #{name}"
end
print_hi('Tom')
#=> prints 'Hi, Tom' to STDOUT.
{% endhighlight %}
Soient $n \in \mathbb{N}$ et $D$ l'application :
$$
\begin{array}{rlll}
D: \mathbb{R}_n[X] & \longrightarrow & \mathbb{R}_n[X] \\
P & \longrightarrow & P^{\prime}
\end{array}
$$
Check out the [Jekyll docs][jekyll-docs] for more info on how to get the most out of Jekyll. File all bugs/feature requests at [Jekyll’s GitHub repo][jekyll-gh]. If you have questions, you can ask them on [Jekyll Talk][jekyll-talk].
1. Vérifier que $D$ est un automorphisme de $\mathbb{R}_n[X]$
2. On pose $\Gamma = id_{\mathbb{R}_n[X]} + D + D^2 + ... + D^n$. Montrer que $\Gamma$ est un automorphisme.
3. Rappeler une factorisation usuelle de $1 - X^{n+1}$
4. En déduire $\Gamma \circ (id - D)$
5. En déduire l'application réciproque de $\Gamma$
[jekyll-docs]: https://jekyllrb.com/docs/home
[jekyll-gh]: https://github.com/jekyll/jekyll
[jekyll-talk]: https://talk.jekyllrb.com/
=======
---
layout: post
title: "Welcome to Jekyll!"
date: 2024-07-01 12:19:36 +0200
categories: jekyll update
---
You’ll find this post in your `_posts` directory. Go ahead and edit it and re-build the site to see your changes. You can rebuild the site in many different ways, but the most common way is to run `jekyll serve`, which launches a web server and auto-regenerates your site when a file is updated.
#### Corrigé :
Jekyll requires blog post files to be named according to the following format:
1. $D$ est un endomorphisme car $D$ est linéaire, et $P' \in \mathbb{R}_n[X]$
2. $\Gamma$ transforme la base canonique de $\mathbb{R}_n[X]$ en famille libre de $\mathbb{R}_n[X]$, de dimension $n+1$. On peut donc dire que $\Gamma$ est une application linéaire (car somme d'applications linéaires), bijective, de $\mathbb{R}_n[X]$ vers $\mathbb{R}_n[X]$, donc $\Gamma$ est un automorphisme.
3. $(1-X^{n+1}) = (1-X) . \sum_{k=0}^n X^k$ TMTC
4. En réécrivant l'égalité précédente en plissant un peu les yeux, on obtient :
$\Gamma \circ (id - D) = (id - D^{n+1})$
Il est alors important de remarquer que dans $\mathbb{R}_n[X]$, $D^{n+1} = 0$. On en déduit alors que dans $\mathbb{R}_n[X]$, $\Gamma \circ (id - D) = id$
`YEAR-MONTH-DAY-title.MARKUP`
Where `YEAR` is a four-digit number, `MONTH` and `DAY` are both two-digit numbers, and `MARKUP` is the file extension representing the format used in the file. After that, include the necessary front matter. Take a look at the source for this post to get an idea about how it works.
Jekyll also offers powerful support for code snippets:
{% highlight ruby %}
def print_hi(name)
puts "Hi, #{name}"
end
print_hi('Tom')
#=> prints 'Hi, Tom' to STDOUT.
{% endhighlight %}
Check out the [Jekyll docs][jekyll-docs] for more info on how to get the most out of Jekyll. File all bugs/feature requests at [Jekyll’s GitHub repo][jekyll-gh]. If you have questions, you can ask them on [Jekyll Talk][jekyll-talk].
[jekyll-docs]: https://jekyllrb.com/docs/home
[jekyll-gh]: https://github.com/jekyll/jekyll
[jekyll-talk]: https://talk.jekyllrb.com/
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