[Fly]

Oops, I misread row for column the first time. The first thing you wanted to do is look at the transpose of your matrix. In the transpose matrix, the ith column vector is the ith row vector of the original matrix.

Below is how to express a column vector as a linear combo of the others.

Let A be an m x n matrix with column vectors A1,...,An

Let x be a n x 1 vector with entries x1,...,xn.

If A*x = 0 ( m x 1 zero vector), then A1*x1 + A2*x2 + .... + An*xn = 0. Suppose you want to represent A1 as a linear combination of the others. Then A1 = -(A2*x2 + A3*x3 + .... + An*xn) / x1.