MathDB

Problem 2

Part of 2013 VJIMC

Problems(2)

matrix, a_(ij)=b_(ij)+1

Source: VJIMC 2013 1.2

5/30/2021
Let A=(aij)A=(a_{ij}) and B=(bij)B=(b_{ij}) be two real 10×1010\times10 matrices such that aij=bij+1a_{ij}=b_{ij}+1 for all i,ji,j and A3=0A^3=0. Prove that det⁡B=0\det B=0.
linear algebramatrix
diagonals of n-hypercube, # of intersection points

Source: VJIMC 2013 2.2

5/31/2021
An nn-dimensional cube is given. Consider all the segments connecting any two different vertices of the cube. How many distinct intersection points do these segments have (excluding the vertices)?
geometry