Question
आव्यूह गुणन, क्रमविनिमेय क्यो नहीं है ?
Answer :
Word Count : 332
आव्यूह गुणन क्रमविनिमेय क्यों नहीं है?
आव्यूह (Matrix) गुणन सामान्य संख्यात्मक गुणन (Multiplication) की तरह क्रमविनिमेय (Commutative) नहीं होता है, अर्थात् यदि AA और BB दो आव्यूह हों, तो यह आवश्यक नहीं कि AB=BAAB = BA हो। इसकी मुख्य वजहें निम्नलिखित हैं:
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आकार (Order) का प्रभाव:
- यदि AA एक m×nm \times n और BB एक n×pn \times p का आव्यूह हो, तो ABAB _____ _______ _________ ____ ________ __________ _________ _____ ________ ________ ________ _______.
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- यदि AA एक m×nm \times n और BB एक n×pn \times p का आव्यूह हो, तो ABAB _____ _______ _________ ____ ________ __________ _________ _____ ________ ________ ________ _______.
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