Question
Download Solution PDFयदि A एक अव्युत्क्रमणीय आव्यूह है, तो A[adj(A)] =?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
एक व्युत्क्रमणीय आव्यूह A के लिए:
- A-1 = \(\rm \frac{adj(A)}{|A|}\)
- |A-1| = |A|-1 = \(\rm \frac{1}{|A|}\)
गणना:
आव्यूह के व्युत्क्रम की परिभाषा से, \({{\rm{A}}^{ - 1}} = \frac{{{\rm{adj}}\left( {\rm{A}} \right)}}{{\left| {\rm{A}} \right|}}\)
दोनों पक्षों को A से गुणा करने पर हमें प्राप्त होता है:
A(A-1) = \(\rm \frac{A[adj(A)]}{|A|}\)
⇒ |A| I = A[adj(A)]
लेकिन यह दिया जाता है कि A एक अव्युत्क्रमणीय आव्यूह है, अर्थात |A| = 0
∴ A[adj(A)] = 0, या A[adj(A)] एक शून्य आव्यूह है।
Last updated on May 30, 2025
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