Without expanding, show that the value of each of the following determ

1.	Without expanding, show that the value of each of the following determinants is zero :\(\begin{vmatrix}49 & 1 & 6 \\[0.3em]39 & 7 & 4 \\[0.3em]26 &2 & 3\end{vmatrix}\)
Answer» Let Δ = \(\begin{vmatrix}49 & 1 & 6 \\[0.3em]39 & 7 & 4 \\[0.3em]26 &2 & 3\end{vmatrix}\) Applying, C₁→C₁ – 8C₃ ⇒ Δ = \(\begin{vmatrix}1 & 1 & 6 \\[0.3em]7 & 7 & 4 \\[0.3em]2 &2 & 3\end{vmatrix}\) As, C₁ = C₂ hence, the determinant is zero.

Without expanding, show that the value of each of the following determinants is zero :\(\begin{vmatrix}49 & 1 & 6 \\[0.3em]39 & 7 & 4 \\[0.3em]26 &2 & 3\end{vmatrix}\)

Answer»

Let Δ = \(\begin{vmatrix}49 & 1 & 6 \\[0.3em]39 & 7 & 4 \\[0.3em]26 &2 & 3\end{vmatrix}\)

Applying,

C₁→C₁ – 8C₃

⇒ Δ = \(\begin{vmatrix}1 & 1 & 6 \\[0.3em]7 & 7 & 4 \\[0.3em]2 &2 & 3\end{vmatrix}\)

As,

C₁ = C₂ hence, the determinant is zero.