Determinants ( help needed )

any one ???

\begin{vmatrix} p &b &c\\ a &q &c \\ a &b &r \end{vmatrix}

R₂-------------->R₂ - R₃

\begin{vmatrix} p &b &c\\ 0 &q-b &c-r \\ a &b &r \end{vmatrix}

R₃-------------->R₃ - R₁

\begin{vmatrix} p &b &c\\ 0 &q-b &c-r \\ a-p &0 &r-c \end{vmatrix}

Taking (p-a)(q-b)(r-c)common from C₁, C₂, C₃ respectively we get....

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

expanding along R₁

pp - a + bq - b + cr - c = 0

or

pp - a + b + q - qq - b + c + r - rr - c = 0

or

pp - a + qq - b - 1 + rr - c - 1 = 0

or..

pp - a + qq - b + rr - c = 2

answer....

simply Gr8 SANDIPAN [1][1]