# det(A) where A is 3x3 matrix

• Nov 26th 2011, 01:01 PM
page929
det(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!
• Nov 26th 2011, 01:43 PM
Also sprach Zarathustra
Re: det(A) where A is 3x3 matrix
Quote:

Originally Posted by page929
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!

Hint:

http://www.analyzemath.com/Tutorial-...erminant_5.gif
• Nov 26th 2011, 01:52 PM
uasac
Re: det(A) where A is 3x3 matrix
$A=\begin{bmatrix}a&b&c\\ d&e&f\\ g&h&i\end{bmatrix}$

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

$\det(A)=a(ei-fh)-b(di-fg)+c(dh-eg)$

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.
• Nov 26th 2011, 02:57 PM
Deveno
Re: 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).