This is one of my favorite problems from my first term of real analysis. This will probably take a few hours. Focus on finding examples, even if you don't have a rigorous proof.
[math]\det [x^2 + y^2, x, y, 1;[/math]
[math]x_1^2 + y_1^2, x_1, y_1, 1;[/math]... (more)