MathDB

In the

xOy

system, consider the collinear points

A_i(x_i,y_i),\ 1\le i\le 4

, such that there are invertible matrices

M\in \mathcal{M}_4(\mathbb{C})

such that

(x_1,x_2,x_3,x_4)

and

(y_1,y_2,y_3,y_4)

are their first two lines. Prove that the sum of the entries of

M^{-1}

doesn't depend of

M

.
Marian Andronache

Problem Statement