Question

Find the value of :
$\left[\begin{array}{ccc}1&2&3\\-4&3&6\\2&-7&9\end{array}\right]$.



DONT SPAM! ☺

Answer 1

We must know :-

$\sf{D=\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] }$

$\sf{\longrightarrow D=a_1 \left[\begin{array}{ccc}b_2&c_2\\b_3&c_3\end{array}\right] -b_1 \left[\begin{array}{ccc}a_2&c_2\\a_3&c_3\end{array}\right]+c_1 \left[\begin{array}{ccc}a_2&b_2\\a_3&b_3\end{array}\right] }$

$\sf{\longrightarrow D=a_1(b_2c_3-b_3c_2)-b_1(a_2c_3-a_3c_2)+c_1((a_2b_3-a_3b_2)}$

_____________________

Now, according to the given question :-

$\sf{\left[\begin{array}{ccc}1&2&3\\-4&3&6\\2&-7&9\end{array}\right] }$

$\sf{ =1 \left[\begin{array}{ccc}3&6\\-7&9\end{array}\right] -2\left[\begin{array}{ccc}-4&6\\2&9\end{array}\right]+3 \left[\begin{array}{ccc}-4&3\\2&-7\end{array}\right] }$

$\sf{=(27+42)-2(-36-12)+3(28-6)}$

$\sf{=69+96+66}$

$\sf{=231}$

Therefore, the answer is 231.

Answer 2

$according \: to \: the \: given \: question :- \\ \\ </p><p></p><p>\begin{gathered}\sf{[\begin{array}{ccc}1&2&3\\-4&3&6\\2&-7&9\end{array}] }\end{gathered} \\ \\ </p><p></p><p>\begin{gathered}\sf{ =1 [\begin{array}{ccc}3&6\\-7&9\end{array}] -2[\begin{array}{ccc}-4&6\\2&9\end{array}]+3 [\begin{array}{ccc}-4&3\\2&-7\end{array}] }\end{gathered} \\ \\ =1[3−769]−2[−4269]+3[−423−7] \\ \\ </p><p></p><p>\sf{=(27+42)-2(-36-12)+3(28-6)} \\ \\ =(27+42)−2(−36−12)+3(28−6) \\ \\ </p><p></p><p>\sf{=69+96+66 }\\ \\ </p><p></p><p>\sf{=231}</p><p></p><p>$