Question
Download Solution PDFयदि \( \begin{vmatrix} 2 & 3+i & -1 \\ 3-i & 0 & i \\ -1 & -i & 1 \end{vmatrix} = A + iB \)
जहाँ i= \(\sqrt{-1 }\) है, तो A + B किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFगणना:
सारणिक Δ = \(a(ei−fh)−b(di−fg)+c(dh−eg)\)
अब, हमारे आव्यूह के लिए,
\(a=2,b=3+i,c=−1,d=3−i,e=0,f=i,g=−1,h=−i,i=1\)
उपसारणिकों की गणना करें
⇒ \( ei−fh=(0)(1)−(i)(−i)=0−(−1)=1\)
⇒ \(di−fg=(3−i)(1)−(i)(−1)=3−i+i=3\)
⇒ \(dh−eg=(3−i)(−i)−(0)(−1)=−3i+i 2=−3i−1=−1−3i\)
⇒ Δ = \(2(1)−(3+i)(3)+(−1)(−1−3i)\)
⇒ Δ = \(2−9−3i+1+3i\)
⇒ \(Δ=−6+0i\)
चूँकि हमें दिया गया है कि वास्तविक और काल्पनिक भागों की तुलना करने पर, हम पाते हैं:
A = -6 और B = 0
इस प्रकार A + B = -6 + 0 = - 6
इसलिए, सही उत्तर विकल्प 2 है।
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