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Question

Mathematics Question on Determinants

The value of ∣123 −436 2−79∣\begin{vmatrix}1&2&3\\\ -4&3&6\\\ 2&-7&9\end{vmatrix} is

A

213

B

-231

C

231

D

39

Answer

231

Explanation

Solution

∣123 −436 2−79∣=1∣36 −79∣−2∣−46 29∣+3\begin{vmatrix}1&2&3\\\ -4&3&6\\\ 2&-7&9\end{vmatrix} = 1 \begin{vmatrix}3&6\\\ -7&9\end{vmatrix} -2 \begin{vmatrix}-4&6\\\ 2&9\end{vmatrix} + 3
∣−43 2−7∣\begin{vmatrix}-4&3\\\ 2&-7\end{vmatrix}
=1(3×9−6(−7))−2(−4×9−2×6)+3((−4)(−7)−3×2)= 1 (3 \times 9 - 6 (-7)) -2 (-4 \times 9 -2 \times 6) +3 ((-4) (-7) - 3 \times 2)
=(27+42)−2(−36−12)+3(28−6)=231= (27 + 42) -2 (-36 - 12)+3 (28 - 6) = 231