g(x) =[2^x/3]

6. Numpy.linalg https://numpy.org/doc/stable/reference/generated/numpy.linalg. solve.html. Generate a random, square matrix and random vector using numpy and then solve using numpy.linalg.solve(). Confirm it is a solution using 'A.dot (x)' where x is the solution from solve(). import numpy as np n=100 Numpy has its own black-box linear system solver numpy.linalg.solve(): A=np.random.rand (n,n) b=np.random.rand (n,1) I

Create an R function pwfun(), which computes values of the piece-wise (mathematical) function pwfun defined in the following way: x < -1 Its graph is as follows. e pwfun(c(-2, 0.5, 3)) 208 pwfun(x) = - x = c(-3, -2, -1, 0, 1, 2, 3.2) pwfun(x) 4 2 0 0 0 39.24 -2x-2 0 x²-1 18 Your R function pwfun() should also accept x as a vector of arbitrary length and return vector of the same length with entries defined as values of the mathematical function pwfun, evaluated at the corresponding entries of vector x. Here are some input vectors and what you should get as a corresponding output. pufun(-1) .-1≤x≤1 1

Question 5 Refer to the following graph and choose the option that reflects the row for node 3 of the D(2) matrix generated by the Floyd-Warshall Algorithm. If you are solving this programmatically, be careful about zero-based indices in most languages. The graph below has 1-based indexing. 1 O 32042-8 3 O-42 327620 -5 Infinity O 87 Infinity 9 0 Infinity O 0204-1-8 10 5 -8