Question
Download Solution PDFएक व्युत्क्रमणीय आव्यूह M के संदर्भ में, निम्नलिखित पर विचार कीजिए:
I.
II.
III.
उपर्युक्त में से कितने सही है?
Answer (Detailed Solution Below)
Detailed Solution
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कथन I
\( |M^2| = |M \times M| = |M| \cdot |M| = |M|^2 \)
⇒ कथन I सही है।
कथन II
एक व्युत्क्रमणीय आव्यूह के लिए, \( M \times M^{-1} = I \), जहाँ \( I \) इकाई आव्यूह है।
\( |M| \cdot |M^{-1}| = |I| = 1 \)
⇒ कथन II गलत है जब तक कि \( |M| = \pm 1 \) न हो।
कथन III
एक आव्यूह का सारणिक उसके परिवर्त आव्यूह के सारणिक के बराबर होता है:
\( |M| = |M^T| \)
⇒ कथन III सही है।
तीनों कथनों में से, दो सही हैं: I और III
इसलिए, सही उत्तर विकल्प 3 है।Last updated on Jul 8, 2025
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