A square matrix in which all the entries below the main diagonal are zero is called upper triangular. Write a function IsMatrix UpperTriangul ar which takes a matrix and returns true if the matrix is upper triangular and false otherwise. For example, matrix A shown below is upper triangular while matrix Bis not upper triangular. -1 5 -1 7 Matrix A -1 7 -1 -9 7 Matrix B 2. 2.
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- IN PYTHON! Given an n×n matrix A and n×1 right-hand side b, write a function that carries out q iterations of the Gauss elimination outer loop (without pivoting), where q is an integer between 1 and n, and returns the resulting augmented matrix with all below-diagonal elements transformed to zero in the left-most q columns. ##The code format given below may help # def gaussq (A, b, q): '''Apply Gauss elimination (without pivoting) to first q columns of a given linear system Inputs: A, coefficient matrix, size n by n b, vector of constants, n by 1 q, number of columns to apply Gauss elimination to, an integer between 1 and n Output: Aa, augmented matrix with all below-diagonal elements transformed to zero in the left-most q columns, n by n+1 #to check the workin c++ please Write a function called Replace All that cerpts two parameters a matrix of 100 elements of type inter and an interval y. The function must - Replace every positive matrix element by the values +5and Replace every negative matrix element by the value - 5 and - Replace every mero try the value y.(a) Write a function matrix_multiply(mat1, mat2) that takes two matrices and returns the result of the matrix multiplication between mat1 and mat2. If the two matrices are not compatible with multiplication, then None should be returned. (b) Write a function print_sums(list1, list2) that takes two equal-length lists of numbers and prints all the sums of the corresponding elements. Thus the first line is the sum of the first element of list1 and the first element of list2, the second line is the sum of the second elements, and so on.
- in python: Write a function that takes in as an input a 2D numpy array, i.e., a matrix (let us label this ?) andan integer ? >0. The function should verify that the inputs are of valid type.The output is a matrix (call this ?) with the same shape as ?. Each element of ? at row ? andcolumn ? is the average of the neighboring elements at the same location in the matrix ?. Theextent of this neighborhood spans rows ?−?,⋯,?−1,?,?+1,⋯,?+? and columns ?−?,⋯,?−1,?,?+1,⋯,?+?. In other words, the neighborhood is a submatrix centered aroundthe location ?, ? with 2?+1 rows and columns. For the boundary elements, assume the matrix ispadded with requisite number of zeros for the purpose of computing the average.C++ Given an integer matrix of size M × N. Find the number of the first of its columns containing an equal number of positive and negative elements (zero elements of the matrix must be ignored). If there are no such columns, then print 0. Write a function to solve this problem. void max_each_column(int a[20][20], int n, int m) 3 3 1 2 -3 4 0 3 7 -8 0 Output: 1Write a function that takes a matrix of order 3 and prints the transpose of it. The transpose should be stored in a different matrix.Test the function in main().For example:Matrix =1 2 34 5 67 8 9Transpose =1 4 72 5 83 6 9 write code for it in c++
- Please Help me With This Problem Write a function to find the norm of a matrix. The norm is defined as the square root of the sum of squaresof all elements in the matrixWrite a function called hw3_problem1 that takes a matrix A of positive integers as its sole input. If the assumption is wrong, the function returns an empty matrix. Otherwise, the function doubles every odd element of A and returns the resulting matrix. Notice that the output matrix will have all even elements. For example, the call B = hw3_problem1([1 4; 5 2; 3 1], will make B equal to [2 4; 10 2; 6 2]. You are not allowed to use loops.: Write a small matrix library The library should have the following functions: double sumOfRow(const double mat[][MAX_COL], const int row, const int maxRow); double sumOfCol(const double mat[][MAX_COL], const int column, const int maxRow); void fillWithRandomNum(double mat[][MAX_COL], const int maxRow); void printMatrix(const double mat[][MAX_COL], const int maxRow);
- A C_++ program for Solving system of linear equations with two variables using Cramer’s rule. In mathematics the coefficientsof linear equations are represented in the form of matrices. A matrix is a two-dimensional array inprogramming. The steps of Cramer’s rule to solve the system of equations are: Step 1: Determining the coefficient matrix from linear equations e.g.a1x+b1y=d1a2x+b2y=d2Coefficient matrix: D =Step 2: Determining the constant column C =Step 3: Finding determinant |D| = (a1*b2) - (b1*a2) and checking if |D| is not equal to zero then do thefollowing:1. Determining X-matrix: DX =The coefficients of the x−column are replaced by the constant columna1 b1a2 b2d1d2d1 b1d2 b22. Determining Y-matrix: Dy =The coefficients of the Y−column are replaced by the constant column3. To solve for x: x=|DX|/|D|4. To solve for y: y=|Dy|/|D|Note that if |D|=0 then the matrix is singular and solving the system of equationis not possible.You’re required to automate all these steps by writing a…Given a square matrix of size ?×?n×n that only contains integers, compute the sum of the two diagonals. If the dimension of the square matrix is odd, make sure that you are not double-counting the value at the centre of the matrix. Figure 2: Sum of diagonals. Function specifications Arguments: matrix (numpy.ndarray) →→ input matrix to be used for computing the sum. Return: sum (int) →→ return the sum of the two diagonals. def sum_of_diagonals(matrix): returnThe vector x ∈ R N has L different entries. For example, L = 4 for x = [3,4,4,5,3,1,5,3]T . One can express x as x = S u, where u ∈ R L satisfies (u)i < (u)j if i < j and S is a matrix that contains only zeros and ones. Write the function repeated_entries, which takes x as input and returns S and u.