If A is 3x3 with all entries 1's and 0's, what is the max value of det(A)?

I answered it to be 1, which is wrong. Can someone help me?

Thanks!

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- November 26th 2011, 02:01 PMpage929det(A) where A is 3x3 matrix [SOLVED]
If A is 3x3 with all entries 1's and 0's, what is the max value of det(A)?

I answered it to be 1, which is wrong. Can someone help me?

Thanks! - November 26th 2011, 02:43 PMAlso sprach ZarathustraRe: det(A) where A is 3x3 matrix
- November 26th 2011, 02:52 PMuasacRe: det(A) where A is 3x3 matrix

Use Laplace's formula on the first row and you'll get

since each entry can only be either 1 or 0, just try to find the coefficients such that you are always summing and not subtracting. You will find that the answer to your question is 2. - November 26th 2011, 03:57 PMDevenoRe: det(A) where A is 3x3 matrix
[1 1 0]

[0 1 1]

[1 0 1] maximizes the positive contributions, and minimizes the negative contributions. (seeing is believing).