variables in a matrix

I was wondering if there might be a way to solve for variables in a matrix. I have the following matrix and need to find a, b, c, and d in the following matrix when it has a rank of 5.

M2=[-1 1 0 0 0 0 0 a b -2*a -2*b 3*a 3*b;
    0 0 1 0 0 a b -a -b a b -a -b;
    0 0 -1 0 0 -a -b a b -a -b a b;
    0 0 0 -1 1 c d -c -d c d -c -d;
    0 0 0 0 0 0 0 0 0 0 0 0 0];

Answer 1

[Walter Roberson]

That matrix will never have rank 5 no matter what the values of the variables are.

The row of all zero at the bottom reduces the maximum row rank by 1, leaving the maximum row rank as 5-1 = 4, so the maximum rank of the matrix overall is at most 4.