FP3- Find the eigenvalues and the eigenvector for the negative eigenvalue, from this 2x2 matrix of columns (2,1) and (3,0)

Let the 2x2 matrix= A. Using the characteristic equation for A (det(A-λI)=0), find the determinant of the matrix (2-λ,1) and (3,-λ). This results in the quadratic λ^2-2λ-3 so λ=3,-1. From the definition of the eigenvector,v, Av=λv. Let v be the column vector (x,y), and for λ=-1 we get the simultaneous equations 2x+3y=x and x=-y, which results in the eigenvector (1,-1).