a) You will create a program that repeatedly multiplies a matrix by a point and plots...

 

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a) You will create a program that repeatedly multiplies a matrix by a point and plots the data to the screen. In this case, we will have a 2D point, (x,y). The point can be represented as a vector: v = [J]. We can also define a 2x2 matrix, M = [a . Computing the product of M with v gives us a new point v': Mv = v'. We can then use v' as the new point, multiply by matrix M again, and get another point, i.e. Mv' = v". This can go on indefinitely, creating a long sequence of points. Create a program that uses numpy to create a matrix and a point. Specifically, you should begin with the point (1, 0), and the matrix: [1.00583 10.087156 1.00156]. Then, repeatedly multiply the matrix by the point to get a new point. You should repeat this between 150 and 250 times. Note: the purpose of this part of the assignment is to get practice with numpy, so you should use numpy for your operations, even if you find it easier to perform this computation a different way. b) Then, make your program plot the data points, using matplotlib. Be sure to label the axes, and include a title. Your title should give a brief description of the shape that the points "trace"do out. Go to Settings to a a) You will create a program that repeatedly multiplies a matrix by a point and plots the data to the screen. In this case, we will have a 2D point, (x,y). The point can be represented as a vector: v = [J]. We can also define a 2x2 matrix, M = [a . Computing the product of M with v gives us a new point v': Mv = v'. We can then use v' as the new point, multiply by matrix M again, and get another point, i.e. Mv' = v". This can go on indefinitely, creating a long sequence of points. Create a program that uses numpy to create a matrix and a point. Specifically, you should begin with the point (1, 0), and the matrix: [1.00583 10.087156 1.00156]. Then, repeatedly multiply the matrix by the point to get a new point. You should repeat this between 150 and 250 times. Note: the purpose of this part of the assignment is to get practice with numpy, so you should use numpy for your operations, even if you find it easier to perform this computation a different way. b) Then, make your program plot the data points, using matplotlib. Be sure to label the axes, and include a title. Your title should give a brief description of the shape that the points "trace"do out. Go to Settings to a