Question

what is cramers paradox?

Answer 1

http://en.wikipedia.org/wiki/Cramer's_paradox

Answer 2

An algebraic plane curve is a locus of points with orthogonal coordinates x,y such that C(x,y) = 0 where C is a polynomial with constant complex coefficients. The degree of a curve is the highest sum of the powers of x and y appearing in any single term of the polynomial. For example, the curve corresponding to x4y3 - 9x2y + 3xy2 - 5 = 0 is of degree 7. The most general polynomial of degree d consists of terms of the form cijxiyj for non-negative integers i,j with i + j £ d. There is just a single term with i + j = 0, and two terms with i + j = 1, and three terms with i + j = 2, and so on. Therefore the general polynomial of degree d consists of 1 + 2 + ... + d + (d+1) = (d+1)(d+2)/2 terms, each with an independent coefficient. However, equating this polynomial to zero, we can divide through by any one of the (non-zero) coefficients, thereby reducing the number of arbitrary coefficients by one. Thus we have (d+1)(d+2)/2 - 1 = d(d+3)/2 free coefficients.