Question
Download Solution PDFयदि A =
1. A + adj A एक शून्य आव्यूह है
2. A−1 + adj A एक शून्य आव्यूह है
3. A − A−1 एक शून्य आव्यूह है
नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि एक आव्यूह A =
व्याख्या:
यदि A =
A का सहगुणनखंड आव्यूह निम्न द्वारा दिया जाता है,
सहगुणनखंड (A) =
तो, A =
(सहगुणनखंड आव्यूह का स्थानांतरण)
⇒ adj A = - A __(i)
⇒ adj A + A = 0 एक शून्य आव्यूह है
अत: कथन 1 सही है।
अब, पंक्ति 1 के साथ A का विस्तार करते हुए,
|A| = 1(-cos2θ - sin2θ) = -1
⇒ A-1 =
⇒ A-1 + adj A = 0 __(ii)
तो, कथन 2 सही है।
(i) का मान (ii) में रखने पर,
⇒ A-1 - A = 0
या A - A-1 = 0
तो, कथन 3 सही है।
Last updated on Jun 18, 2025
->UPSC has extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.