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Question 30: Write a C++ program to solve the following positive definite linear system using the Cholesky's method. For simplification, specify the linear system within the program. 1.7%. 1.1x2 + 2.7x, = -1.1x2 + 1.6x2 1.9x, 2.7%. 1.9x2 + 4.5x, 7.39 -3.36 12.03 #include #include using namespace std; #define n 3 Il number of unknowns int main() { char quit; inti..k; double a[n][n] = {{1.7.-1.1, 2.7}, {-1.1, 1.6, -1.9}. {2.7.-1.9, 4.5}}; double b[n] = {7.39, -3.36, 12.03} : 1/ right hand side constant vector double x[n]; double (nn). Y[n].sum ; Processing Section // Formation of Land U as factors of A, i.e., A=LU for(i=0;i=0; i--) { sum = 0.0 ; for(j=i+1 ; j> quit; return 0; } Question 07: Write a C++ program to find the dominant eigenvalue of the following matrix using the power method. For simplification, specify the matrix within the program. Take x - [1, 1, 1]" as the initial approximation. The iterations of the method should stop when either the approximation is accurate within 10-, or the number of iterations exceeds 100, whichever happens first 4 1 2 5 0 L7 2 1 #include #include using namespace std; 50 #define n 3 #define TOL 0.00001 #define N 100 // number of components // error tolerance // maximum number of iterations int main() char quit; inti. j.r.k; double a[n][n] = { {4,1,0}. {2,5,0}. (7,2,1}}; // the problem matrix double x[n] = { 1, 1, 1); // initial approx. to the dominant eigenvector double xp[n], sum, sumi , B, err: - Processing Section for ( k=1; k abs(x[-])) r=; B = x[r]: for(i=0;i> a[i][i]: cout> b[i]; Question 30: Write a C++ program to solve the following positive definite linear system using the Cholesky's method. For simplification, specify the linear system within the program. 1.7%. 1.1x2 + 2.7x, = -1.1x2 + 1.6x2 1.9x, 2.7%. 1.9x2 + 4.5x, 7.39 -3.36 12.03 #include #include using namespace std; #define n 3 Il number of unknowns int main() { char quit; inti..k; double a[n][n] = {{1.7.-1.1, 2.7}, {-1.1, 1.6, -1.9}. {2.7.-1.9, 4.5}}; double b[n] = {7.39, -3.36, 12.03} : 1/ right hand side constant vector double x[n]; double (nn). Y[n].sum ; Processing Section // Formation of Land U as factors of A, i.e., A=LU for(i=0;i=0; i--) { sum = 0.0 ; for(j=i+1 ; j> quit; return 0; } Question 07: Write a C++ program to find the dominant eigenvalue of the following matrix using the power method. For simplification, specify the matrix within the program. Take x - [1, 1, 1]" as the initial approximation. The iterations of the method should stop when either the approximation is accurate within 10-, or the number of iterations exceeds 100, whichever happens first 4 1 2 5 0 L7 2 1 #include #include using namespace std; 50 #define n 3 #define TOL 0.00001 #define N 100 // number of components // error tolerance // maximum number of iterations int main() char quit; inti. j.r.k; double a[n][n] = { {4,1,0}. {2,5,0}. (7,2,1}}; // the problem matrix double x[n] = { 1, 1, 1); // initial approx. to the dominant eigenvector double xp[n], sum, sumi , B, err: - Processing Section for ( k=1; k abs(x[-])) r=; B = x[r]: for(i=0;i> a[i][i]: cout> b[i]<><><><><><>