3. Use the script PlaneTransform2.m to explore the way matrices transform the plane. To dothis, set up a 2 × 2 matrix, A, in Matlab with the command: >> A = [1 0.5; 0.25 1]Also, set a number of transform steps (just one step for now) >> NumIters=1;Now, when you type: >> [Aout]=PlaneTransform2(A,NumIters);, the Matlab program willtake in the A matrix and the desired number of iterations and will generate a bunch ofvectors, x, plotted as dots around the unit circle, and then calculate the transformed vectors,Ax. The “before” and “after” vectors will be plotted so that you can see how the matrixtransforms vectors in the plane (Notice that the vectors that start out on the x and y axeshave an asterisk and a circle plotted at their ends. You should also be able to envision thatthe matrix is really transforming the entire plane). Try this process with a number of differentmatrices:

\gg \mathbf{A}=[\cos (p i / 32), \sin (p i / 32) ;-\sin (p i / 32), \cos (p i / 32)] Comment on what you observe for each case. (Don't be afraid to run it again with the samematrix, to see the original vectors alone, before the transformed vectors are added.)