Download NCERT Solutions for Class 12 Mathematics Chapter 03 आव्यूह
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Question 1: आव्यूह \( A \) तथा \( B \) एक दूसरे के व्युत्क्रम होंगे केवल यदि
(A) \( AB = BA \)
(B) \( AB = BA = 0 \)
(C) \( AB = 0, BA = I \)
(D) \( AB = BA = I \)
Answer:
व्युत्क्रमणीय आव्यूह की परिभाषा के अनुसार, यदि \( A \) और \( B \) एक-दूसरे के व्युत्क्रम हैं, तो उनका गुणनफल एक तत्समक आव्यूह (Identity matrix) \( I \) होना चाहिए।
अर्थात, \( AB = BA = I \)
अतः विकल्प (D) सही है।
मुख्य बिंदु:
• दो आव्यूह \( A \) और \( B \) परस्पर व्युत्क्रम कहलाते हैं यदि \( AB = BA = I \) हो।
• यहाँ \( I \) समान कोटि का तत्समक आव्यूह है।
• आव्यूह गुणन हमेशा क्रमविनिमेय (Commutative) हो यह आवश्यक नहीं है, परंतु व्युत्क्रम के लिए यह शर्त आवश्यक है कि दोनों तरफ से गुणा करने पर तत्समक आव्यूह प्राप्त हो।
आम गलतियाँ:
• केवल \( AB = I \) देखकर उत्तर चुन लेना, जबकि \( BA = I \) होना भी उतना ही आवश्यक है।
• \( AB = BA = 0 \) या अन्य विकल्पों को सही मान लेना।
• व्युत्क्रम आव्यूह और शून्य आव्यूह की परिभाषा में भ्रमित होना।
Exam Tips:
a) बहुविकल्पीय प्रश्नों में सभी विकल्पों को ध्यान से पढ़ें।
b) व्युत्क्रम आव्यूह की मूल परिभाषा \( AA^{-1} = A^{-1}A = I \) को हमेशा याद रखें।
c) ऐसे सैद्धांतिक प्रश्नों का उत्तर देते समय रीतिकरण से बचें और परिभाषा का प्रयोग करें।
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Mathematics Class 12 Curriculum Solutions: Chapter 03 आव्यूह
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FAQs
The complete and updated NCERT Solutions Class 12 Maths Chapter 03 Matrices (आव्यूह) Exercise 3.4 in Hindi is available for free on StudiesToday.com. These solutions for Class 12 Mathematics are as per latest NCERT curriculum.
Yes, our experts have revised the NCERT Solutions Class 12 Maths Chapter 03 Matrices (आव्यूह) Exercise 3.4 in Hindi as per 2026 exam pattern. All textbook exercises have been solved and have added explanation about how the Mathematics concepts are applied in case-study and assertion-reasoning questions.
Toppers recommend using NCERT language because NCERT marking schemes are strictly based on textbook definitions. Our NCERT Solutions Class 12 Maths Chapter 03 Matrices (आव्यूह) Exercise 3.4 in Hindi will help students to get full marks in the theory paper.
Yes, we provide bilingual support for Class 12 Mathematics. You can access NCERT Solutions Class 12 Maths Chapter 03 Matrices (आव्यूह) Exercise 3.4 in Hindi in both English and Hindi medium.
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