- #1

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- Thread starter skymariner
- Start date

- #1

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- #2

disregardthat

Science Advisor

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could you explain this a little better? Do you mean that the matrix have entries 1,2,3,...,n^2, and do all appear and only once?

- #3

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Yes, the entries consist of all the numbers 1 to n^2 and each number occurs only once.

- #4

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- 5

[tex]

\left|\begin{array}{cc}

1 & 2 \\

3 & 4

\end{array}\right| = 4 - 6 = -2

[/tex]

[tex]

\left|\begin{array}{cc}

1 & 2 \\

4 & 3

\end{array}\right| = 3 - 8 = -5

[/tex]

[tex]

\left|\begin{array}{cc}

1 & 3 \\

2 & 4

\end{array}\right| = 4 - 6 = -2

[/tex]

[tex]

\left|\begin{array}{cc}

1 & 3 \\

4 & 2

\end{array}\right| = 2 - 12 = -10

[/tex]

[tex]

\left|\begin{array}{cc}

1 & 4 \\

2 & 3

\end{array}\right| = 3 - 8 = -5

[/tex]

[tex]

\left|\begin{array}{cc}

1 & 4 \\

3 & 2

\end{array}\right| = 2 - 12 = -10

[/tex]

I don't see how to generalize it at this point. I would think we need to add the biggest numbers [itex]n^{2}, (n - 1)^{2}, \ldots, n^{2} - n +1[/itex] along the main diagonal, then the next along the third to the main diagonal and start inserting the smallest elements along the odd diagonals.

- #5

AlephZero

Science Advisor

Homework Helper

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- 293

When n >= 3, the minimum absolute value of the determinant is 0.

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