If Δ=35678910x5, then x105536879 equal to:

Given Δ=35678910x5 using properties of determinants⇒ Δ=(−1)536879x105⇒ Δ=(−1)2536x105879⇒ Δ=(−1)3x105536879=−Δ

If Δ=35678910x5, then x105536879 equal to:

Given Δ=35678910x5 using properties of determinants⇒ Δ=(−1)536879x105⇒ Δ=(−1)2536x105879⇒ Δ=(−1)3x105536879=−Δ

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If $Δ = |\begin{array}{ccc} 3 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & x & 5 \end{array}|, then |\begin{array}{ccc} x & 10 & 5 \\ 5 & 3 & 6 \\ 8 & 7 & 9 \end{array}|$ equal to:

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$- Δ$

$Δx$

$Δ$

answer is B.

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Detailed Solution

Given $Δ = |\begin{array}{ccc} 3 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & x & 5 \end{array}|$ using properties of determinants

$\begin{array}{l} \Rightarrow Δ = (- 1) |\begin{array}{ccc} 5 & 3 & 6 \\ 8 & 7 & 9 \\ x & 10 & 5 \end{array}| \\ \Rightarrow Δ = (- 1)^{2} |\begin{array}{ccc} 5 & 3 & 6 \\ x & 10 & 5 \\ 8 & 7 & 9 \end{array}| \\ \Rightarrow Δ = (- 1)^{3} |\begin{array}{ccc} x & 10 & 5 \\ 5 & 3 & 6 \\ 8 & 7 & 9 \end{array}| = - Δ \end{array}$