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March 22nd, 2019, 11:00 PM   #1
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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.
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March 22nd, 2019, 11:33 PM   #2
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This should be moved to the Linear Algebra forum
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March 22nd, 2019, 11:57 PM   #3
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Quote:
Originally Posted by romsek View Post
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,

Integrator
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