Consider the Initial Value Problem: dx/dt =[-3,-5;5,-3)]x, x(0)=[3;4] (a) Find the eigenvalues and eigenvectors for the coefficient matrix. \lambda _(1)=,vec(v)_(1)=[,], and \lambda _(2)=,vec(v)_(2)=[,] (b) find the solutuion to the initial value problem. Give your solution in real form. x_(t)= [ ] . Determine the shape and orientation of solution curves algebraically. spiral, spiraling outward in the counterclockwise orientation 1.Describe the trajectory