Question
Download Solution PDFसमीकरण 2x + y = 5; x - 3y = -1 और 3x + 4y = k के निकाय संगत हैं, तो k बराबर है :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
2x + y = 5; x - 3y = -1 और 3x + 4y = k संगत है
प्रयुक्त संकल्पना:
यदि निकाय संगत है तो A की रैंक (आव्यूह गुणांक) = संवर्धित आव्यूह (A: B) की रैंक = n (चरों की संख्या)
गणना:
\(\left|\begin{array}{ccc} 2 & 1 & 5 \\ 1 & -3 & -1 \\ 3 & 4 & k \end{array}\right|\)
⇒ R2 = 2R2 - R1
⇒ R3 = 2R3 - 3R1
\(\left|\begin{array}{ccc} 2 & 1 & 5 \\ 0 & -7 & -7 \\ 0 & 5 & 2k - 15 \end{array}\right|\)
⇒ R3 = 7R3 + 5R2
\(\left|\begin{array}{ccc} 2 & 1 & 5 \\ 0 & -7 & -7 \\ 0 & 0 & 14k - 140 \end{array}\right|\)
14k - 140 = 0 A और A:B की रैंक के लिए = चरों की संख्या अर्थात 2
∴ k = 10
अत: सही विकल्प 4 है।
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