Let D(x,y) denote the determinant of the 2x2 matrix with rows x and y. Assume the vectors v1,v2, v3 in R2 are pairwise linearly independent. Prove that D(v2, v3)v1 + D(v3, v1) v2 + D(v1, v2)v3=0.
(Hint: write v1 as a linear combination of v2 and v3 and use Cramer's rule to solve for the coefficients.)
I'm not sure how to set this up as linear combination. I've been trying, but I must be doing something wrong because its not making much sense.