Analyzing The Matrix

Algebra Level 5

det(pbcaqcabr)=0\large \det\begin{pmatrix} p & b & c\\ a & q & c\\ a & b & r\\ \end{pmatrix}=0

In the determinant above ap,bq,cra\neq p , b\neq q , c\neq r, find the value of ppa+qqb+rrc\dfrac{p}{p-a}+\dfrac{q}{q-b}+\dfrac{r}{r-c}.

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