Answer: b. 231
Step-by-step explanation:
Determinant of any Matrix A=[tex]\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right][/tex] is given by :-
[tex]\begin{vmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{vmatrix}\\\\=a_{11}(a_{22}a_{33}-a_{23}a_{32})-a_{12}(a_{21}a_{33}-a_{23}a_{31})+a_{13}(a_{21}a_{32}-a_{22}a_{31})[/tex]
Similarly,
[tex]\begin{vmatrix}1&2&3\\ -4&3& 6\\2&-7& 9\end{vmatrix}[/tex]
[tex]=1(3\times9-6\times-7)-2(-4\times9-6\times2)+3(-4\times-7-3\times2)\\\\=69-2(-48)+3(22)=69+96+66=231[/tex]
Hence, b is CORRRECT answer.
