Inverse Matrix

Eine quadratische Matrix A heißt invertierbar , wenn es eine Matrix A − 1 MathType@MTEF@& 053;@& 053;@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC 0xbbL8F4rqWrFfpeea0xe9Gq=Jc9qspeea0xb9as=JfrVkFHe9pgea 0dXdar=tb9fs0dXdab6hc9qr0=yr0=vqpWqaaeaabaGaaiaacaqabe aadaabauaaaOqaaabaaaaaaaaapeGaamyqa8aadaahaaWcbeqaa8qa cqGHsislcaaIXaaaaaaa@4024@ gibt, sodass A ⋅ A − 1 = E MathType@MTEF@& 053;@& 053;@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC 0xbbL8F4rqWrFfpeea0xe9Gq=Jc9qspeea0xb9as=JfrVkFHe9pgea 0dXdar=tb9fs0dXdab6hc9qr0=yr0=vqpWqaaeaabaGaaiaacaqabe aadaabauaaaOqaaabaaaaaaaaapeGaamyqaiabgwSixlaadgeapaWa aWbaaSqabeaapeGaeyOeI0IaaGymaaaakiabg2da9iaadweaaaa@450E@ gilt. A − 1 MathType@MTEF@& 053;@& 053;@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC 0xbbL8F4rqWrFfpeea0xe9Gq=Jc9qspeea0xb9as=JfrVkFHe9pgea 0dXdar=tb9fs0dXdab6hc9qr0=yr0=vqpWqaaeaabaGaaiaacaqabe aadaabauaaaOqaaabaaaaaaaaapeGaamyqa8aadaahaaWcbeqaa8qa cqGHsislcaaIXaaaaaaa@4024@ heißt Inverse zu A. Beispiel : Die Inverse zu der Matrix A = ( 1 2 2 3 ) MathType@MTEF@& 053;@& 053;@+= feaagKart1ev2aaatCvAUfeB