PYTHON /JUPYTER NOTEBOOKS Program a backward solver (i.e. write your code) for an upper triangular system Ux=b. The algorithm is attached below for Numpy and Python with offset 1. Recall that NumPy and Python have offset 0 for their sequence data types.

Python

The point P has coordinates x = -3 m and y = 4 m relative to the origin O. The vector v is v = -4î + 4î m/s. Matlab Mathematica Python SymPy from sympy import * Px = -3 Py = 4 v = Matrix([-4, 4, 0]) copy this text What is the orthogonal projection of v onto the vector û = -ếg associated with the polar coordinates for point P? Proj(t, й) — e î+ e jm/s

Write a recursive Python function named pgcd, to find and return the Greatest Common Divisor (GCD) of two numbers x and y passed in parameters. • Test it gcd (1234,4321) gcd (8192,192)

IN PYTHON I want a code in python and no need to post work on paper Iwant a screenshot of the code A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557. The following code format should help: def td(l, m, u, b):   '''Solve a linear system Ax = b where A is tridiagonal      Inputs: l,…

Midterm Practice Problems 1. Use recursion to write a function count_ones that returns how many Is there are in a number n when represented in decimal (base 10). For example, 1231 has two 1s. You can assume that n is nonnegative and at most 9 digits long. Do not use global (or static) variables. In main perform at least three tests of count_ones and use assert to check that the returned value is correct. Your function should have the following prototype: // count_ones (n) returns the number of is in the decimal representation of n // requires: 0 <= n < 10^9 int count_ones (int n);

6. X is (a,b,c,d), Y is {1,2,3,4). {(a,1), (b,2), (c,2), (d,4)) is a function from X to Y.

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