Question
निम्नलिखित आव्यूहों के लिए, जाँच कीजिए कि ऐसे व्युत्क्रमणीय आव्यूह प का अस्तित्व होता है जिसके लिए P-1AP विकर्ण है। जब ऐसे P का अस्तित्व होता है तब P ज्ञात कीजिए।
Answer :
Word Count : 437
किसी \( n \times n \) आव्यूह \( A \) के लिए, यदि कोई व्युत्क्रमणीय आव्यूह \( P \) मौजूद हो जिससे कि \( P^{-1} A P \) विकर्णीय (\( D \)) हो, तो इसका अर्थ है कि \( A \) विकर्णीकरणीय है। ### विकर्णीकरणीयता की शर्तें किसी आव्यूह \( A \) को विकर्णीकरणीय करने के लिए: 1. \( A \) के लिए लक्षणिक बहुपद \( |A - \lambda I| = 0 _____ _______ ______ ________ ____ __________ _____.
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किसी \( n \times n \) आव्यूह \( A \) के लिए, यदि कोई व्युत्क्रमणीय आव्यूह \( P \) मौजूद हो जिससे कि \( P^{-1} A P \) विकर्णीय (\( D \)) हो, तो इसका अर्थ है कि \( A \) विकर्णीकरणीय है। ### विकर्णीकरणीयता की शर्तें किसी आव्यूह \( A \) को विकर्णीकरणीय करने के लिए: 1. \( A \) के लिए लक्षणिक बहुपद \( |A - \lambda I| = 0 _____ _______ ______ ________ ____ __________ _____.
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