March 22nd, 2019, 10:00 PM  #1 
Member Joined: Aug 2018 From: România Posts: 54 Thanks: 3  Determinants
Hello all, Let $\displaystyle P, Q, R : \mathbb C \rightarrow \mathbb C$ polynomial functions of degré $\displaystyle \leq 2$ and $\displaystyle a, b, c \in \mathbb C$ such that $\displaystyle \left\begin{matrix}P(a)&Q(a)&R(a)\\P(b)&Q(b)&R(b) \\P(c)&Q(c)&R(c)\end{matrix}\right=1$. Calculate the sum: $\displaystyle S=\left\begin{matrix}P(1)&Q(1)&R(1)\\P(b)&Q(b)&R( b)\\P(c)&Q(c)&R(c)\end{matrix}\right + \left\begin{matrix}P(a)&Q(a)&R(a)\\P(1)&Q(1)&R(1) \\P(c)&Q(c)&R(c)\end{matrix}\right + \left\begin{matrix}P(a)&Q(a)&R(a)\\P(b)&Q(b)&R(b) \\P(1)&Q(1)&R(1)\end{matrix}\right$. All the best, Integrator Last edited by Integrator; March 22nd, 2019 at 10:43 PM. 
March 22nd, 2019, 10:33 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,452 Thanks: 1337 
This should be moved to the Linear Algebra forum

March 22nd, 2019, 10:57 PM  #3 
Member Joined: Aug 2018 From: România Posts: 54 Thanks: 3  Hello, Thousands of apologies!I changed the first sentence and so be read : "Let $\displaystyle P, Q, R : \mathbb C \rightarrow \mathbb C$ polynomial functions of degré $\displaystyle G\leq 2$ and $\displaystyle a, b, c \in \mathbb C$ such that..." All the best, Integrator 

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