Question

Consider the determinant $\Delta =\left|\begin{array}{ccc}{a}_1& a_2& a_3\\ b_1& b_2& b_3\\ c_1& c_2& c_3\end{array}\right|$

$M_{ij}=$ Minor of the element of $i^{th}$ row & $j^{th}$ column.

$C_{ij}=$ Cofactor of element of $i^{th}$ row & $j^{th}$ column.

If all the elements of the determinant are multiplied by 2, then the value of new determinant is

• A. $0$
• B. $8\Delta$
• C. $2\Delta$
• D. $2^9\Delta$

Answer 1

The correct option is B $8\Delta$

Let ${△}^1=\left|\begin{array}{ccc}{2a}_1& {2a}_2& {2a}_3\\ {2b}_1& {2b}_2& {2b}_3\\ {2c}_1& {2c}_2& {2c}_3\end{array}\right|$

Taking $2$ common from $R_1,R_2$ and $R_3$

${△}^1=\mathrm{2.2.2}\left|\begin{array}{ccc}{a}_1& a_2& a_3\\ b_1& b_2& b_3\\ c_1& c_2& c_3\end{array}\right|=8△$