6. Evaluate the determinant for the following matrix: 1 O A.8 O B.-2 O C.5 O D.-4 3.
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- Draw the graph from the adjacency matrix given below. Handwritten please.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…Replace the first row of matrix Y to vector b , b=[4 6 8 10]
- Given a 2-D square matrix: ant mat{3}[{3]={{1, 2 3} {4,586}, {7.8.9FF Write a function transpose which Create a 3*3 matrix trans and store the transpose of given matrix in it.And prxnt the ' transpose, IN C++.Enter the 5 × 5 Hilbert matrix using MATLAB software 1 1/ 2 1/ 3 1/ 4 1/ 5 1/ 2 1/ 3 1/ 4 1/ 5 1/ 6 1/ 3 1/ 4 1/ 5 1/ 6 1/ 7 1/ 4 1/ 5 1/ 6 1/ 7 1/ 8 1/ 5 1/ 6 1/ 7 1/ 8 1/ 9 H i) Find the determinant of H. ii) Find the transpose and inverse of H iii) Using the commands in the text, find the dimensions of H, the column sums, and the row sums of H.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 column a1 b1a2 b2d1d2 d1 b1d2 b2 2. 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 program…
- In the following matrix, identify the coefficient, variable, and constant. 3x 5y 9 2x 3y 5What is the LU factorisation of the following matrixI do not understand this expression. so is c[i][j] += a[i][h] * b[h][j] mean c[i][j] = a[i][h] * b[h][j] + c[i][j]?? ; We do not know about the + matrix c right?