Consider an autoregressive system represented by a first-order difference equation
y[n]=0.5y[n−1]+x[n],n≥0

a. Find the impulse response h[n] of the system

b. Compute the response of the system to x[n]=u[n]−u[n−3] using the convolution sum.

c. Verify results with MATLAB.

d. Determine the stability of the system using Matlab.