Without expanding, evaluate the following determinants. [(1, a, b+c) (1, b, c+a) (1, c, a+b)]

Question

Without expanding, evaluate the following determinants.

\(\begin{vmatrix}-1&1&2\\-2&3&-4\\-3&4&0\end{vmatrix}\)

[(1, a, b+c) (1, b, c+a) (1, c, a+b)]

Answer 1

Let D = \(\begin{vmatrix}1&a&b+c\\1&b&c+a\\1&c&a+b\end{vmatrix}\)

Applying C₃ → C₃ + C₂ , we get .