Finding minimum from matrix Consider following $3\times 3$ matrix.
$\begin{pmatrix}3&6&9\\
    2& 4 &8\\
    1 &5& 7
    \end{pmatrix}$
I need to find combination of three numbers where each number comes from unique column & row. 
For example $3,6,8$ is not what I want as $3$ and $6$ are from same row.
$6,4,7$ is also not right because $6$ and $4$ are from same columns.
$3,4,7$ is valid as each number comes from different column and row.
Next thing I want, is to find combination whose sum is minimum compared to sum of all other possible combinations. For example $3,4,7$ will be final answer if $3+4+7 = \min$. How do I find this for $n \times n$ matrix? 
 A: This is known as the assignment problem.  The best-known algorithm for solving it is the Hungarian algorithm.
A: Per the previous answer, this is a linear assignment problem. Here is a simple way to solve it (not necessarily the fastest executing for very large n).
If you have MATLAB, you can download YALMIP for free.
Let A = n by n matrix of interest.
x = binvar(n,n,'full') % x defined to be a not necessarily symmetric n by n matrix of zeros and ones, which is the matrix of optimization variables specifying which entries of A are to be chosen (1 if chosen, 0 if not).
optimize([sum(x,2) == 1, sum(x,1) == 1],sum(sum(x.*A))) % Solves the problem
Note that in optimize command,
sum(x,2) == 1 constrains row sums to 1
sum(x,1) == 1 constrains column sums to 1
sum(sum(x.*A)) is the objective to be minimized
value(x) provides the optimal selection matrix
value(sum(sum(x.*A)))) provides the optimal score.

For your example
n = 3
A = [3 6 8;3 4 8;2 5 7]

value(x) is 
 1     0     0

 0     1     0

 0     0     1

Optimal score is 14.
If you want to maximize the sum, you could just change the optimize command to optimize([sum(x,2) == 1, sum(x,1) == 1],-sum(sum(x.*A))) which minimizes the negative of the sum.
Here's a random 5 by 5 matrix:

0.8147    0.0975    0.1576    0.1419    0.6557
0.9058    0.2785    0.9706    0.4218    0.0357
0.1270    0.5469    0.9572    0.9157    0.8491
0.9134    0.9575    0.4854    0.7922    0.9340
0.6324    0.9649    0.8003    0.9595    0.6787


Optimal (producing minimum sum) x is
0     1     0     0     0
0     0     0     0     1
1     0     0     0     0
0     0     1     0     0
0     0     0     1     0
Optimal score is 1.7051.
