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 March 22nd, 2019, 11:00 PM #1 Senior Member   Joined: Aug 2018 From: România Posts: 108 Thanks: 7 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 11:43 PM. March 22nd, 2019, 11:33 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,633 Thanks: 1472 This should be moved to the Linear Algebra forum March 22nd, 2019, 11:57 PM   #3
Senior Member

Joined: Aug 2018
From: România

Posts: 108
Thanks: 7

Quote:
 Originally Posted by romsek This should be moved to the Linear Algebra forum
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,

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