Question

Solve the determinant:

$\left|\begin{array}{ccc}1& a& a^2-bc\\ 1& b& b^2-ac\\ 1& c& c^2-ab\end{array}\right|$

• A. $0$
• B. $a^3+b^3+c^3-3abc$
• C. $3abc$
• D. $(a+b+c{)}^3$

Answer 1

The correct option is A $0$

$\left[\begin{array}{ccc}1& a& a^2-bc\\ 1& b& b^2-ac\\ 1& c& c^2-ac\end{array}\right]$

As one column have same elements i.e $1$.

Hence the value of given Determinant is ${}^{\prime }{0}^{\prime }$