a) Plot the data points with a circle marker (Python). b) Plot the unique interpolating polynomial of maximum order (passes exactly through each point) and print the equation of the polynomial (in the form y = an xn+ an-1xn-1 + ... + a1x + a0) to the screen using python. Don't use polyfit & polyval for this problem; use the given data points to construct the matrix form for the unknowns and solve it using python to find the polynomial coefficients. c) compute the linear spline equation for each segment by hand. Include the domain. Plot the individual linear spline for every interval using python d) Plot the "not-a-knot" cubic spline (python). Make sure b,c & d are shown in different colors. Include a legend on the graph. Make observations from the final plot with all the curves. -2012 3 8 25 52 36 y-10 3

python please provide code and result Create a random 5x5 matrix sampled from the unit interval in variable “A". Compute the inverse of the matrix, and store it in variable "B". Using matrix multiplication, compute the product of the two matrices - make sure you got identity matrix with 1 on the diagonal and 0 elsewhere (up to numerical precision). Plot the matrices as heatmaps with matplotlib imshow function. Use one plot with 3 subplots, add subplot titles ("A", "A-inverse", "I").

The following equation can be used to compute values of y as a function of x: y=be¯ªsin(bx) (0.0012x¹ −0.15x³ +0.075x² +2.5x) where a and b are parameters. (a) Write Python code to compute a vector y for a = 2, b = 5, and x as a vector with values from 0 to π/2 in increments Ax= π/40. (b) Compute the vector z = y² with element-by-element-wise operations. (c) Combine x, y, and zinto a 3-column matrix W.(Hint use np. hstack function) (d) Generate a plot of y and z versus x. Include a title, axis labels, and a legend. For the y versus x curve, format a solid blue line. For the z versus x curve, choose a magenta dashed line. Include grid lines.

Play and practice all the functions that we listed here.  What I would like you to do is to first create three vectors---a logic vector, a double vector, and a character vector, for example, x1 = c( TRUE, FALSE, TRUE) x2 = c( 0, -2.5, 1, 3, 5.9 ) x3 = c( "a1", "a2", "za", "zz", "0", "1") and apply each function to all three vectors to see what would happen. If the function requires more than one input x, then you just create other objects as needed. sum (x) sum of the elements of x prod (x) product of the elements of x max (x) maximum of the elements of x min(x) minimum of the elements of x which. max (x) returns the index of the greatest element of x which. min(x) returns the index of the smallest element of x range (x) id. than c (min(x), max (x)) length (x) number of elements in x mean (x) mean of the elements of x median (x) median of the elements of x   round (x, n) rounds the elements of x to n decimals rev…