Question

If $\begin{vmatrix} a_1 &b_1 &c_1 \\\[0.3em] a_2 &b_2 &c_2 \\\[0.3em] a_ 3&b_3 &c_3 \end{vmatrix}=\,\,\,\,3,\,$ then $\begin{vmatrix} 3a_1 &9b_1 &3c_1 \\\[0.3em] a_2 &3b_2 &c_2 \\\[0.3em] 3a_ 3&9b_3 &3c_3 \end{vmatrix}=$,

• A. 51
• B. 27
• C. 81
• D. 91

Answer 1

Answer: (C)

81

Answer 2

$\begin{vmatrix} 3a_1 &9b_1 &3c_1 \\\[0.3em] a_2 &3b_2 &c_2 \\\[0.3em] 3a_ 3&9b_3 &3c_3 \end{vmatrix}= 9 \begin{vmatrix} a_1 &b_1 &c_1 \\\[0.3em] a_2 &b_2 &c_2 \\\[0.3em] a_ 3&b_3 &c_3 \end{vmatrix}$
= $9 \times 3 \begin{vmatrix} a_1 &b_1 &c_1 \\\[0.3em] a_2 &b_2 &c_2 \\\[0.3em] a_ 3&b_3 &c_3 \end{vmatrix} = 27 \times 3 = 81$