Question

If each row of a determinant of third order of value $\Delta$ is multipled by 3, then the value of new determinant is

• A. $\Delta$
• B. $27\Delta$
• C. $21\Delta$
• D. $54\Delta$

Answer 1

The correct option is B $27\Delta$

$\Delta =\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|$
Now for $\left|\begin{array}{ccc}{3a}_1& {3b}_1& {3c}_1\\ {3a}_2& 3b_2& {3c}_2\\ {3a}_3& 3b_3& {3c}_3\end{array}\right|$
Taking out $3$ common from $R_1,R_2,R_3$
$=3\times 3\times 3=\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=27\Delta$