Miklos Schweitzer 1950_6
Source: first round of 1950
October 2, 2008
linear algebralinear algebra unsolved
Problem Statement
Prove the following identity for determinants:
|c_{ik} \plus{} a_i \plus{} b_k \plus{} 1|_{i,k \equal{} 1,...,n} \plus{} |c_{ik}|_{i,k \equal{} 1,...,n} \equal{} |c_{ik} \plus{} a_i \plus{} b_k|_{i,k \equal{} 1,...,n} \plus{} |c_{ik} \plus{} 1|_{i,k \equal{} 1,...,n}