Determinant Additional Properties

Q. If $\Delta =\left[\begin{array}{ccc}1& a& bc\\ 1& b& ca\\ 1& c& ab\end{array}\right]$, then which of the following is a factor of $\Delta :$

1. (a + b)
2. (b - c)
3. abc
4. Both b and c

Q. The matrix A = $\left[\begin{array}{cccc}a& 0& 3& 7\\ 2& 5& 1& 3\\ 0& 0& 2& 4\\ 0& 0& 0& b\end{array}\right]$ has det(A) = 100 and trace (A) = 14. The value of |a-b| is ______ .

1. 3