MATLAB: How to find the values of 2 variables that will make the matrix rank 6

MATLABrank symbolic-matrix

I have the following symbolic matrix
M =
 
[  4, -3,  0,  0,  0, 0,  0]
[ -2,  0,  1,  0,  0, 0,  0]
[ -6,  0,  0,  0, 12, 0,  0]
[ -3,  0,  0,  0,  0, 1,  0]
[  0,  6,  0, -8,  0, 0,  0]
[  0,  0,  0,  2,  0, 0, -4]
[  0,  3,  0,  0, -y, 0,  0]
[  0,  0, -5,  x,  0, 0,  0]
I'd like to find any values of x and y that make M rank 6. How do I do this?

Best Answer

for x = -10:1:10
  for y = -10:1:10
    A = [  4, -3,  0,  0,  0, 0,  0
          -2,  0,  1,  0,  0, 0,  0
          -6,  0,  0,  0, 12, 0,  0
          -3,  0,  0,  0,  0, 1,  0
           0,  6,  0, -8,  0, 0,  0
           0,  0,  0,  2,  0, 0, -4
           0,  3,  0,  0, -y, 0,  0
           0,  0, -5,  x,  0, 0,  0] ;
    R = rank(A) ;
    if R == 6
        [x y]
        break
    end
    end
end
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