Suppose that the three numbers r,, 12, and r3 are distinct. Show that the three functions exp (r,x), exp (12x), and exp (r3x) are linearly independent by showing that their Wronskian given below is nonzero for all x. 1 1 1 W= exp [(1 +12+r3)x]* 1 If y1. Y2. y, are n solutions of the homogeneous nth-order linear equation y) + p, (x)y" + Pn - 1(x)y'+P (x)y = 0 on an open interval I, where each p, is continuous. Then the Wronskian is W = W(y,, y2, .., yn). If y,, y2. ... yn are linearly independent, then W#0 at each point of I. To simplify W, evaluate the determinant. W= exp [(1 +12 +r3)*]•O