Review Note

Last Update: 05/10/2024 02:51 PM

Current Deck: 2ème année::Maths::MATHCC1::DETERMINANTS

Published

Currently Published Content


Recto
calcul d'inverse à l'aide de la comatrice + démonstration 
Verso
\(A ^{-1} = \frac 1{ \det A} (\operatorname {Com} A )^T \)
\(A = (a_{ij} ) \implies |A| = \sum _{j=1} ^n a_{ij} \underbrace{(-1) ^{i+j} \Delta _{ij} }_{ H_{ij} \text { cofacteur}}\)
\(\operatorname{Com} A = (H_{ij} ) \text{ matrice des cofacteurs ou comatrice de A }\implies A^T \times \mathrm{Com} ~A = (\sum a_ {ik} H'_{kj})= \Bigg\{ \array{\det A , \text{ si i = j } \\ 0 \text{ si i neq j } }\)
m

No published tags.

Pending Suggestions


No pending suggestions for this note.