Question

By using properties of determinants ,show that: \(\begin{vmatrix}0&a&-b\\-a&0&-c\\b&c&0\end{vmatrix}\)=0

Answer 1

We have,
△= \(\begin{vmatrix}0&a&-b\\-a&0&-c\\b&c&0\end{vmatrix}\)
Applying R₁ \(\to\) cR₁,we have

△=\(\frac{1}{c}\begin{vmatrix}0&ac&-bc\\-a&0&-c\\b&c&0\end{vmatrix}\)
Applying R₁1\(\to\) R₁-bR₂,we have

△=\(\frac{1}{c}\begin{vmatrix}ab&ac&0\\-a&0&-c\\b&c&0\end{vmatrix}\)

=\(\frac{1}{c}\begin{vmatrix}b&c&0\\-a&0&-c\\b&c&0\end{vmatrix}\)

Here, the two rows R₁ and R₃ are identical.
∴∆ = 0.