3 6. Evaluate the determinant for the following matrix: 1 O A. 8 ОВ. -2 O C. 5 O D. -4 LO
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- 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.True or False The inverse of a matrix M can be calculated in Python with the command Inverse=np.linalg.inv(M)Draw the following graph as represented in the adjacency matrix below. a b c d A 1 1 1 0 B 0 1 1 0 C 0 0 1 1 d 0 0 0 1
- Replace the first row of matrix Y to vector b , b=[4 6 8 10]Replace the second column of * matrix Y to vector b, b=[4 68 10]— lupdlipanpmtisie et tmts e R 5 A, ) B S S S et Given a 2-D square matrix: B mati31l31-{11, 2 3} 14 5 6}, (7,8,9}}. Write a function transpose which varts the matrix mat into its ftranspose 3np}ae t the transpose, IN C++ language.
- I 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?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…construct a Playfair matrix with the key "largest"
- 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…Find Matrix Chain Multiplication for the following four matrices (M1, M2, M3, and M4) using dynamic programming Technique. Matrix M1 M2 M3 M4 Order of Matrix 5 x 4 4 x 3 3 x 5 5 x 6python 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…