Question
Download Solution PDFमाना कि A और B समान कोटि के दो वर्ग आव्यूह हैं। यदि AB एक शून्य आव्यूह है, तो निम्नलिखित में से कौन सा सही है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है, AB = O
माना कि A =
B =
अब AB =
दोनों पक्षों की तुलना करने पर, हमें प्राप्त होता है
⇒ ap + br = 0...(1)
⇒ aq + bs = 0...(2)
⇒ cp + dr = 0...(3)
⇒ cq + ds = 0...(4)
समीकरणों (i) और (iii) से, हमें प्राप्त होता है:
⇒ (ad - bc)p = 0 और (ad - bc)r = 0
समीकरणों (ii) और (iv) से, हमें प्राप्त होता है:
⇒ (ad - bc) q = 0 और (ad - bc)s = 0
अब, यदि A व्युत्क्रमणीय है।
ad - bc ≠ 0
इसलिए, p = q = r = s = 0
तब, B शून्य आव्यूह है।
∴ विकल्प (c) सही है।
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