Question

If $\left|\begin{array}{ccc}1+ax& 1+bx& 1+cx\\ 1+a_{1}x& 1+b_{1}x& 1+c_{1}x\\ 1+a_{2}x& 1+b_{2}x& 1+c_{2}x\end{array}\right|=A_0+A_{1}x+A_2{x}^2+A_3{x}^3$,
then $A_0$ is equal to

• A. a b c
• B. 1
• C. 0
• D. None of these

Answer 1

Answer: (C)

On putting x = 0 both sides we get
$\left|\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right|=A_0$
$\Rightarrow A_0=0$