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- Given a vector x=[12 3 4 5 . ], take the square of each element and sum them up. What should be the dimension of the vector x so that the squared sum (as above) is as close as possible to 1000 but not more than 1000? ....Write the Python code to find the transitive closure when given zero-one matrix. DO NOT use the Warshall Algorithm in this code. Pseudo code: A := MR B := A for i := 2 to n A:= A ⊙ MR B:= B ∨ A return B (the zero-one matrix for R*)Suppose a computer program needs to apply an affine transformation to a complex three-dimensional object made up of 3000 points. The transformation is composed of 8 matrices (call them M1 through M3), so for each point (x, y, z) in the object, the following operation is performed. |-|-|-|-|| y M1 M2 M3 M7 M8 Each multiplication of a matrix times a column vector involves 16 multiplications (of one number by another) and 12 additions, for a total of 28 arithmetic operations. Each multiplication of a matrix times another matrix involves 64 multiplications and 48 additions, for a total of 112 arithmetic operations. (These numbers are not made up or chosen randomly; they are facts about 4 x 4 matrix multiplication.) The most inefficient way of applying the transformation to the 3000 points would be to begin on the left, multiplying M1 by M2, then that result by M3, and so on along the list from left to right, and doing the same 8 multiplications again for each of the 3000 points. How many…
- USING PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal (i.e., ai,j where j = i) and the ones immediately above and belowit(i.e.,ai,j wherej=i+1orj=i−1). 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. Please show steps and explain.Perform the following vector multiplication of two vectors and find the y-component of the resulting vector, c. č = à xb ā = [ax ay az] b = [b, by b;] where ax = 5, ay = 5, az = 5 and by = 9, by = -7, b, = -8. %3D Your Answer:Write the Python code to find the transitive closure when given zero-one matrix. DO NOT use the Warshall Algorithm in this code.
- suppose a computer solves a 100x100 matrix using Gauss elimination with partial pivoting in 1 second, how long will it take to solve a 300x300 matrix using Gauss elimination with partial pivoting on the same computer? and if you have a limit of 100 seconds to solve a matrix of size (N x N) using Gauss elimination with partial pivoting, what is the largest N can you do? show all the steps of the solutionSparse matrix-vector multiplication in Python is similar to numpy.dot operation, however the provided @ operator is used. Let us consider multiplying a 5 by 5 sparse matrix with a 5 by 3 sparse matrix shown below. 01000 00010 10001 10000 01000 100 001 x 000 010 100 The Python code to implement multiplication of these two sparse matricesThe goal of this problem is to walk from cell (0, 0) to cell (m, n) of a two-dimensional array. Each step must be either to the right or downward. So you can step from cell (1, 1) to cell (1, 2) or (2, 1). but not from (1, 1) to (0, 1) or (1,0). You are given a toll matrix, where each cell contains a toll that must be paid upon entry into that cell. The goal is to make it from cell (0, 0) to cell (m, n) while paying the smallest possible total toll. Does a greedy algorithm work? Think it out. Write a dynamic programming algorithm that finds the minimum possible total toll. It does not need to do reconstruction and say how to achieve that total toll.
- Create a 3-by-3 matrix. A = [1 7 3; 2 9 12; 5 22 7]; Calculate the right eigenvectors, V, the eigenvalues, D, and the left eigenvectors, W. [V,D,W] eig(A) %3!This is discrete math: Find f ? g and g ? f , where f (x) = x^2 + 1 and g(x) = x + 2, are functions from R to RWrite the following set of equations in matrix form (or array form): 50=5x₂ - 7x₂ 4x₂ + 7x₂ +30=0 x₁ - 7x₂ = 40-3x₂ + 5x₁ Use Python to solve for the unknowns. In addition, compute the transpose and inverse of the coefficient matrix.