Solve the given initial-value problem. x' = 1 2 0 1 − 1 2 x, x(0) = 2 7

I'll go out on a limb and guess the system is



with initial condition . The coefficient matrix has eigenvalues such that



The corresponding eigenvectors are such that







So the characteristic solution to the ODE system is



When , we have



from which it follows that and , making the particular solution to the IVP

Idon't see any graph, however the graph of the function : f(x) = x²-2x+3 is a parabola: 1) open upward (since a> 0)2) it intersects y-axis in 3 (y=3)3) its axis of symmetry is x = +1 ( -b/2a)4) it's minimum is y = -2, so its vertex is (1,-2)5) it doesn't intersect the x-axis since discriminant < 0