(20 points) The response of a Linear Time Invariant system to a given input is shown below:
$x[n] = \left(\frac{1}{4}\right)^n u[n]$, $y[n] = 5 \left(\frac{3}{4}\right)^n u[n]$
a. Determine the impulse response, $h[n]$ of the system.
b. Determine the output of the system, $y[n]$, if the input is $x[n] = \left(\frac{1}{3}\right)^n u[n]$.
c. Use Matlab to check and verify your results (must provide the output responses, as well as
the scripts for generating any work, a clean script or m-file, do not include unnecessary
code/output).