The sequence, w, is defined by the second-order, linear, homogeneous, difference equation shown below: w[k+2]-7 w[k+1]+12 w[k]=0 w[0]=2, \quad w[1]=-2, \quad w[2]=-38, \quad w[3]=-242 a) Write down the z-transform for

the LDE and obtain an expression for: \frac{W(z)}{z} b) Hence, solve the LDE using partial fractions and inverse z-transforms.