Question
Download Solution PDF\(\left| {\begin{array}{*{20}{c}} 1&1&1\\ 1&{1 + {\rm{a}}}&1\\ {1 + {\rm{b}}}&1&1 \end{array}} \right|\) का मूल्य क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
प्राथमिक पंक्ति या स्तंभ रूपांतरण आव्यूह के सारणिक के मूल्य को नहीं बदलते हैं।
गणना:
\(\left| {\begin{array}{*{20}{c}} 1&1&1\\ 1&{1 + {\rm{a}}}&1\\ {1 + {\rm{b}}}&1&1 \end{array}} \right|\)
R2 → R2 – R1, R3 → R3 – R1 लागू करके हमें मिलता है
= \(\left| {\begin{array}{*{20}{c}} 1&1&1\\ 0&{\rm{a}}&0\\ {\rm{b}}&0&0 \end{array}} \right|\)
अब C3 के साथ विस्तार करके
= 1 (0 – ab) – 0 + 0 = -ab
Last updated on Jun 30, 2025
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