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| author | martial.simon <martial.simon@epita.fr> | 2025-04-13 19:54:19 +0200 |
|---|---|---|
| committer | martial.simon <martial.simon@epita.fr> | 2025-04-13 19:54:19 +0200 |
| commit | 66c3bbfa94d8a41e58adf154be25e6d86fee8e30 (patch) | |
| tree | 9c5e998f324f2f60c1717759144da3f996c5ae1a /PVCM/Rappels matrices.md | |
init: initial commit
Diffstat (limited to 'PVCM/Rappels matrices.md')
| -rwxr-xr-x | PVCM/Rappels matrices.md | 67 |
1 files changed, 67 insertions, 0 deletions
diff --git a/PVCM/Rappels matrices.md b/PVCM/Rappels matrices.md new file mode 100755 index 0000000..5775637 --- /dev/null +++ b/PVCM/Rappels matrices.md @@ -0,0 +1,67 @@ +# Question 1 + +$$ +A = \begin{pmatrix} +1 & 0 & 2 \\ +2 & -1 & 1 \\ +0 & -2 & 1 +\end{pmatrix} = (A_{ij}) +;\; +b = \begin{pmatrix} +-1 \\ +0 \\ +2 +\end{pmatrix} +$$ +$$ +X = Ab = \begin{pmatrix} +1 & 0 & 2 \\ +2 & -1 &1 \\ +0 & -2 & 1 +\end{pmatrix} +\begin{pmatrix} +-1 \\ +0 \\ +2 +\end{pmatrix} += \begin{pmatrix} +3 \\ +0 \\ +2 +\end{pmatrix} +$$ +$$ +\begin{pmatrix} +3 & 1 & 2 \\ +1 & 4 & 3 \\ +0 & 0 & 1 +\end{pmatrix} +\begin{pmatrix} +-2 \\ +0 \\ +2 +\end{pmatrix} += \begin{pmatrix} +-2 \\ +4 \\ +2 +\end{pmatrix} +$$ +# Question 2 +### Matrice de rotation + +$$ +R = \begin{pmatrix} +\cos \theta & -\sin \theta \\ +\sin \theta & \cos \theta +\end{pmatrix} +$$ +### Matrice orthogonale + +$$A^TA = Id$$ +0 + +### Matrice de passage + + +Stage ds secteur + large que annonce
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