If $\begin{vmatrix}-a^2 & ab & ac\\ba & -b^2 & bc\\ac & bc & -c^2 \end{vmatrix}=4x,$ then $x=$
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $a^2b^2c^2$
$\begin{vmatrix}-a^2 & ab & ac\\ba & -b^2 & bc\\ac & bc & -c^2 \end{vmatrix}=4x$
$=abc\begin{vmatrix}-a & b & c\\a & -b & c\\a & b & -c \end{vmatrix}=4x$
$=a^2b^2c^2\begin{vmatrix}-1 & 1 & 1\\1 & -1 & 1\\1 & 1 & -1 \end{vmatrix}=4x$
$R_2→R_2+R_1,R_3→R_3+R_1$
$a^2b^2c^2\begin{vmatrix}-1 & 1 & 1\\ 0&0 & 2\\0 & 2 & 0 \end{vmatrix}=4x$
$4a^2b^2c^2=4x⇒x=a^2b^2c^2$