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- MatrixMultiplication algorithm (A1, A2, ... , An)pre-cond: An instance is a series of n matrices.post-cond: optSol is the bracketing that takes the fewest multiplications, and optCost is the resultant number of multiplications.9. Generated random matrix 3x3 and sort in ascending order of each row 10.Find exact answer for y= x in the interval 0Find a (generating matrix) for the following code and find the parameters [n, k, d], code. C = {10101010, 1100, 11110000,01100110,00111100}algorithm MatrixMultiplication (A1, A2, ... , An) pre-cond: An instance is a sequence of n matrices. post-cond: optSol is a bracketing that requires the fewest multiplications, andoptCost is the resulting number of multiplications.Define, A = Find x. Hint: use numpy.linalg.inv and the @operator for matrix multiplication. 3 6 2 b = 10 5 2 1 7 5 Y = 3 Ax + b = Y Npython Linear Equation SystemLU Decomposition Method AlgorithmDecomposition phase The LU Decomposition (Doolittle) method has the following properties: The U matrix is identical to the upper triangular matrix resulting from the Gaussian Elimination;The elements at the bottom below the main diagonal of the matrix L are the multipliers used during the Gaussian Elimination, that is, Li*j is the multiplier that eliminated Ai*j.It is common practice to store the multipliers at the bottom of the coefficient matrix, replacing the coefficients as they are eliminated (Li*j replacing Ai*j) The diagonal elements of L do not need to be stored, as their values are understood to be unitary. The final form of the coefficient matrix would be the mixture of L and U: The initial part of the LU Decomposition Method algorithm is identified with Gaussian Elimination, except that each λ multiplier is now stored in the lower triangular portion of matrix A: 1)solve the system of linear equations…LANGUAGUE: C I - Write an algorithm that takes two nxn matrices stored in vectors v1 and v2 and, computes a new matrix to be stored in vector v3 that corresponds to multiplication of the matrix stored in vector v1 by the matrix stored in vector v2. Assume that vector v3 is already properly allocated. int MultiplicaMatrizes (int *v1, int *v2, int *v3, int n) II - Write an algorithm for the Pune operation that punishes an element in a stack putting it n positions down. Assume that the stack is implemented as a vector. int Pune(Stack *s, int n) III - Write a k-remove(L,k) algorithm to remove the kth node from the linear list simply chained L void * sllRemovek (SLList *l, int k)Array P = [40, 30, 25, 10, 35, 5, 20] Suppose the dimension of 6 matrices (A1, A2 … A6) are given by array P A1 is a P[0] x P[1] matrix A2 is a P[1] x P[2] matrix . . . A6 is a P[5] x P[6] a) Find the minimum number of scalar multiplications necessary to calculate the product of all the 6 matrices (A1.A2.A3.A4.A5.A6) and show the parenthesization for this multiplication. • Solve the problem manually (you need not to write any code) using bottom-up tabulation approach. Compute and show the ‘m’ matrix and ‘s’ matrix to solve your problem.Linear Equation SystemLU Decomposition Method AlgorithmDecomposition phase The LU Decomposition (Doolittle) method has the following properties: The U matrix is identical to the upper triangular matrix resulting from the Gaussian Elimination;The elements at the bottom below the main diagonal of the matrix L are the multipliers used during the Gaussian Elimination, that is, Li*j is the multiplier that eliminated Ai*j.It is common practice to store the multipliers at the bottom of the coefficient matrix, replacing the coefficients as they are eliminated (Li*j replacing Ai*j) The diagonal elements of L do not need to be stored, as their values are understood to be unitary. The final form of the coefficient matrix would be the mixture of L and U: The initial part of the LU Decomposition Method algorithm is identified with Gaussian Elimination, except that each λ multiplier is now stored in the lower triangular portion of matrix A: solve the system of linear equations followed by the…Sparse 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 formula C=numpy.add(A, B) adds the two matrices A and B and stores the result in C.• To subtract matrix B from matrix A, enter C=numpy.subtract(A, B). The result is stored in C.• C=numpy.divide(A, B): Split matrix A into two equal parts and store the result in C.• C stands for numpy.multiply(A, B): Multiply matrices A and B, then store the result in matrices C.• C=numpy.sum(A): Calculate the sum of each element in the matrix A, then store the result in c R.• C=numpy.sum(A, axis = 0): Create a vector C by adding the columns of the matrix A.• C=numpy.sum(A, axis = 1): Summarize matrix A row-by-row and store the result in the vector C. Create Python code that demonstrates the use of these techniques in a sample matrix.16. Given an n-element array with n > 100, is it possible to find an algorithm that can find an element that is neither the maximum nor the minimum with fewer than 10 comparisons? (a) yes (b) noSEE MORE QUESTIONS