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 = 101: we can also define a 2x2 matrix, m = tlc di comput . 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 : 1.00583 -0.087156] with the point (1,0), and the matrix: . then, repeatedly multiply the "10.087156 1.00583 ) matrix by the point to get a new point. you should repeat this between 150 and 250 times. 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" out.

Write a program that reads in a series of lines of input character by character (using the library function the first line of the input contains an integer which specifies the number of remaining lines of input, each of which contains a floating point number. the integer value on the first line can be read with (the library function) but all of the following lines can only be read with each line, after the first, contains a single floating point value, with up to four digits before the decimal point, and up to four digits following the decimal point, but there is not necessarily a decimal point in each number; i.e., it may appear to be an integer, but the digits should be read by your program, and the number should be converted to a corresponding floating point number. for instance, suppose the following input: 5 3.1255 20.25 0.875 1921.50 31 the required output is: − each of the input floating point values, printed on a separate line with four digits of precision, using printf(); − on the last line of the output, the string “total: ” followed by the sum of the input values, printed with printf() to 4 digits of precision. for example, the total of the sample input given above is 1976.7505, so the required output for this input would be: 3.1255 20.2500 0.8750 1921.5000 31.0000 total: 1976.7505 do not concern yourself with small differences in the total due to rounding, as the grader will not deduct points for this. constraints: − you are not allowed to use arrays on this portion of the lab assignment. − there is no maximum number of lines allowable. it all depends upon the first value of input. since you aren’t saving anything, it doesn’t matter. − you can assume that input will not contain more than 4 digits before or after the decimal point. you do not need to error check for this condition. -you must use getchar() to read in the floating point values one character at a time (i.e. do not use -you must declare and use your floating point values as a double to minimize rounding errors. -only use printf() to output the floating point numbers and the total (do not use − be sure your directions to the user are clear so they are sure to enter the input data correctly.