MathDB

IMC 2006, problem 3, day 1

Source:

July 22, 2006

linear algebramatrixRing TheoryIMCcollege contests

Problem Statement

Let

A

be an

n

x

n

matrix with integer entries and

b_{1},b_{2},...,b_{k}

be integers satisfying

detA=b_{1}\cdot b_{2}\cdot ...\cdot b_{k}

. Prove that there exist

n

x

n

-matrices

B_{1},B_{2},...,B_{k}

with integers entries such that

A=B_{1}\cdot B_{2}\cdot ...\cdot B_{k}

and

detB_{i}=b_{i}

for all

i=1,...,k

.

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