Question

If $\Delta = \begin{vmatrix}3&5&6\\ 7&8&9\\ 10&x&5\end{vmatrix}$, them $ \begin{vmatrix}x&10&5\\ 5&3&6\\ 8&7&9\end{vmatrix} $ equal to:

• A. $\Delta$
• B. $ - \Delta$
• C. $ \Delta x $
• D. 0

Answer 1

Answer: (B)

Given : $\Delta = \begin{vmatrix}3&5&6\\ 7&8&9\\ 10&x&5\end{vmatrix}$
using properties of determinants
$ \Rightarrow \Delta = \left(-1\right) \begin{vmatrix}5&3&6\\ 8&7&9\\ x&10&5\end{vmatrix} $
$ \Rightarrow \Delta = \left(-1\right)^{2} \begin{vmatrix}5&3&6\\ x&10&5\\ 8&7&9\end{vmatrix}$
$ \Rightarrow \Delta =\left(-1\right)^{3}\begin{vmatrix}x&10&5\\ 5&3&6\\ 8&7&9\end{vmatrix} =- \Delta $