I have this matrix:
X Y X*Y X^2 Y^2 Z 11,16 1,24 13,84 124,55 1,54 22,15 24,20 16,23 392,77 585,64 263,41 2,83 19,85 10,72 212,79 394,02 114,92 7,97 10,35 4,11 42,54 107,12 16,89 22,33 19,72 1,39 27,41 388,88 1,93 16,83 0,00 20,00 0,00 0,00 400,00 34,60 20,87 20,00 417,40 435,56 400,00 5,74 19,99 4,62 92,35 399,60 21,34 14,72 10,28 15,16 155,84 105,68 229,83 21,59 4,51 20,00 90,20 20,34 400,00 15,61 0,00 4,48 0,00 0,00 20,07 61,77 16,70 19,65 328,16 278,89 386,12 6,31 6,08 4,58 27,85 36,97 20,98 35,74 25,00 11,87 296,75 625,00 140,90 4,40 14,90 3,12 46,49 222,01 9,73 21,70 0,00 0,00 0,00 0,00 0,00 58,20 9,66 20,00 193,20 93,32 400,00 4,73 5,22 14,66 76,53 27,25 214,92 40,36 11,77 10,47 123,23 138,53 109,62 13,62 15,10 17,19 259,57 228,01 295,50 12,57 25,00 3,87 96,75 625,00 14,98 8,74 25,00 0,00 0,00 625,00 0,00 12,00 14,59 8,71 127,08 212,87 75,86 14,81 15,20 0,00 0,00 231,04 0,00 21,60 5,23 10,72 56,07 27,35 114,92 26,50 2,14 15,03 32,16 4,58 225,90 53,10 0,51 8,37 4,27 0,26 70,06 49,43 25,00 20,00 500,00 625,00 400,00 0,60 21,67 14,36 311,18 469,59 206,21 5,52 3,31 0,13 0,43 10,96 0,02 44,08
And I'm trying to solve it, starting by getting it's determinant (after fill it with "1", so it becomes a square matrix).
I tried using Octave, but I got:
error: det: invalid dense matrix type
And trying in MSExcel 2007 I got a value of zero, what is wrong (I don't know the answer, but I know it can't be zero).
Any idea how to solve it (preferable on the computer)?
--reformulating
I have the above 30 values for X, Y and Z, and I need to find the coeficients (a,b,c,d,e,f) for:
$z=a+bx+cy+dxy+ex^2+fy^2$
(the values for [a, b, c, d, e, f] need to work for all lines at the same time)