Prove that vmatrix 1+a & 1 & 1 1 & 1+b & 1 1 & 1 & 1+c vmatrix = abc ( 1 + 1 a + 1 b…

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

Prove that

\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = abc \left( 1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)

hence find the value of the determinant, if

a, b

and

c

are the roots of the equation

px^3 - qx^2 + rx - s = 0