Question

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

DONT SPAM! ​

Answer 1

$\huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}$

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 :

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

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

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

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

$\sf\fbox\blue{=231}$

Therefore, the answer is 231.

${\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}$

$\red{\tt{sωєєтcнαям♡~}}$

Answer 2

$\huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}$

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

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

Now, according to the given question :

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

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

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

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

$\sf\fbox\blue{=231}$

Therefore, the answer is 231.