Question 838026
<pre>

It does not change the value of a determinant to
multiply a row by a constant and add it
to another row. 

{{{abs(matrix(3,7,

x^"",    "", "","",       y,  "",       1,        
x^2,  "", "","",     y^2,  "",      x+y,       
x^3,  "", "","",      y^3, "",     x^2+xy+y^2))}}} 

Multiply the 2nd row by -x and add it to the 3rd row:

{{{abs(matrix(3,6,

x^"",    "", "",       y,     "",    1,        
x^2,  "", "",     y^2,     "",   x+y,       
0,  "", "",      y^3-xy^2, "",   y^2))}}} 

Multiply the 1st row by -x and add it to the 2nd row:

{{{abs(matrix(3,6,

x^"",    "", "",       y,     "",    1,        
0,  "", "",     y^2-xy,   "",     y,       
0,  "", "",      y^3-xy^2, "",   y^2))}}}

Multiply the 2nd row by -y and add it to the 3rd row:

{{{abs(matrix(3,7,

x^"",    "", "",       y,   "", "",     1,        
0,  "", "",     y^2-xy,   "", "",    y,       
0^"",  "", "",      0, "", "",  0))}}} 

The bottom row has all 0's, so the value of the 
determinant is 0.

Edwin</pre>