There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials than the conventional algorithm described in the previous exercise. It is called Horner's method. This pseudocode shows how to use this method to find the value of anx" + An-1x²-¹ +...+ a₁x + ao = 0 at x = c. procedure Horner(c, ao, a₁, a2,..., an: real numbers) y := an for i:=1 to n y := y*c+an-i return y(y = anc" +an-1-1+...+ a₁c + ao} 2.a Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. 2.b Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)

Using a for-loop in Matlab for the given vectors V=[10, 1, 4, 10, 8]; W=[10, 4, 10, 3, 5]; a) Write a program (using for-loop) that calculates the dot-product, C=(V-W).W b) What is the value of C? Choices 214 |-9 |-36 |-13

Please use python and show codes

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,…