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3x3 matrix - find max {det A}

Source: Romanian IMO Team Selection Test TST 1987, problem 1

September 25, 2005
linear algebramatrixabsolute valuelinear algebra unsolved

Problem Statement

Let a,b,ca,b,c be distinct real numbers such that a+b+c>0a+b+c>0. Let MM be the set of 3×33\times 3 matrices with the property that each line and each column contain all given numbers a,b,ca,b,c. Find {max⁡{det⁡A∣A∈M}\{\max \{ \det A \mid A \in M \} and the number of matrices which realise the maximum value. Mircea Becheanu
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