यदि A= , f(x) = x2 - 2x - I है, तो f(A) का मान क्या है?

Answer (Detailed Solution Below)

Option 1 :
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Agniveer Navy SSR Full Test - 01
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संकल्पना:

माना कि f(x) = a0 xn + axn-1 + a2 xn-2 + ... + an-1 x + an एक बहुपद है और माना कि आव्यूह A कोटि n वाली एक वर्ग आव्यूह है। तो, 

f(A) = a0 An + a1 An-1 + a2 An-2 + ... + an-1 A + an Iको आव्यूह बहुपद कहा जाता है। 

गणना:

दिया गया है, A =  औरf(x) = x2 - 2x - I  

आव्यूह A कोटि 2 वाली वर्ग आव्यूह है, तो यह दिए गए बहुपद को संतुष्ट करती है। 

⇒ f(A) = A2 - 2A - I

⇒ f(A) = A A - 2A - I 

⇒ f(A) =  - 2  -   

⇒ f(A) =  -  - 

⇒ f(A) =  -  

⇒ f(A) =  

सही विकल्प 1 है।

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