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Question 24: Write a C++ program to solve the following linear system using the Doolittle's method. For simplification, specify the linear system within the program. 1.7x1 + 2.3x2 1.5x3 2.35 1.1x1 + 1.6x2 1.9x3 -0.94 2.7% 2.2x2 + 1.5x3 2.70 #include using namespace std; #define n 3 int main() { char quit ; int i, j,s; double a[n][n] = {{1.7, 2.3, -1.5}, {1.1, 1.6, -1.9}, {2.7, -2.2, 1.5}}; double b[n] = {2.35, -0.94, 2.7}; // right-hand side constant vector double x[n]; double u[n][n], [n][n],y[n], sum ; - // 11 Processing Section // Formation of L and 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; Remark: Replace the lines 9 and 10 in the solution of Question 24 with the following code segment to receive che linear system at the execution time (instead of fixing in the code). 1/-- Input Section cout> a[i]; cout> b[i]: Question 27: Write a C++ program to solve the following linear system using the Crout's method. For simplification, specify the linear system within the program, 1.7%. + 2.3x 1.5x, = 2.35 1.1x, + 1.6%; 1.9x, = -0.94 2.7%, 2.2%, + 1.5x, = 2.70 #include using namespace std; #define n 3 // number of unknowns int main() { char quit; int i, j,s double a[n][n] = {{1.7, 2.3, -1.5), (1.1, 1.6, -1.9}, {2.7, -2.2, 1.5}} ; double b[n) - {2.35, -0.94, 2.7); // right hand side constant vector double x[n]; double u[n][n], [n][n], [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; } Remark: Replace the lines 9 and 10 in the solution of Question 27 with the following code segment to receive the linear system at the execution time (instead of fixing in the code). Input Section cout> a[0]: cout> b[i]; Problem 14. solve the following linear system AX - using the Cholesky's method. 1.7%, - 1.1%, + 2.7x2 - 7.39 -1.1x+ 1.6X3 1.9x3 - -3.36 2.7*. - 1.94, + 4.5x; - 12.03 The required solution vector is given by, x-(1.0999, 2.1, 2.9) 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*: - -1.1% + 2.7%. - 1.14 + 2.7x3 - 1.6x, - 1.9x2 - -3.36 1.94, + 4.5x, - 12.03 #include #include using namespace std; #definen 3 Il number of unknowns Int main() 1 char quit Int!..k double an] - ((1.7.-1.1, 2.7).(-1.1, 1.6 -1.93. (2.7.-1.9.4.53 double b[n) - 17.39, -3.36, 12.03); // right hand side constant vector double xn! double nin). Yn). sum: //--................... Processing Section - // Formation of Land U as factors of A. I... A-LU for ( 0;len; I++ ) for (1-0:1++) 100] -0.0: COTO) - sart atoo)): for (1-1::-) 010) -as)[0]/ICO): for(i=1;i // Forward substitution phase for solving LY-B ( - )) YO) - b[0] / 0) for (-1; In: I++ ) { sum - 0.0 ; for (1-0-1-1; ++) sum-sum + 100 Yll: y[I] - ( i] - sum ) / ION : } // Back Substitution Phase for solving LT X=Y (* = [y: - Eyes: 1,2]) x[n-1] = y[n-1] /[[n-1][n-1]; for(i=n-2; i>=0; i--) { sum = 0.0 ; for(j=i+1; j> quit: return 0; } Question 24: Write a C++ program to solve the following linear system using the Doolittle's method. For simplification, specify the linear system within the program. 1.7x1 + 2.3x2 1.5x3 2.35 1.1x1 + 1.6x2 1.9x3 -0.94 2.7% 2.2x2 + 1.5x3 2.70 #include using namespace std; #define n 3 int main() { char quit ; int i, j,s; double a[n][n] = {{1.7, 2.3, -1.5}, {1.1, 1.6, -1.9}, {2.7, -2.2, 1.5}}; double b[n] = {2.35, -0.94, 2.7}; // right-hand side constant vector double x[n]; double u[n][n], [n][n],y[n], sum ; - // 11 Processing Section // Formation of L and 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; Remark: Replace the lines 9 and 10 in the solution of Question 24 with the following code segment to receive che linear system at the execution time (instead of fixing in the code). 1/-- Input Section cout> a[i]; cout> b[i]: Question 27: Write a C++ program to solve the following linear system using the Crout's method. For simplification, specify the linear system within the program, 1.7%. + 2.3x 1.5x, = 2.35 1.1x, + 1.6%; 1.9x, = -0.94 2.7%, 2.2%, + 1.5x, = 2.70 #include using namespace std; #define n 3 // number of unknowns int main() { char quit; int i, j,s double a[n][n] = {{1.7, 2.3, -1.5), (1.1, 1.6, -1.9}, {2.7, -2.2, 1.5}} ; double b[n) - {2.35, -0.94, 2.7); // right hand side constant vector double x[n]; double u[n][n], [n][n], [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; } Remark: Replace the lines 9 and 10 in the solution of Question 27 with the following code segment to receive the linear system at the execution time (instead of fixing in the code). Input Section cout> a[0]: cout> b[i]; Problem 14. solve the following linear system AX - using the Cholesky's method. 1.7%, - 1.1%, + 2.7x2 - 7.39 -1.1x+ 1.6X3 1.9x3 - -3.36 2.7*. - 1.94, + 4.5x; - 12.03 The required solution vector is given by, x-(1.0999, 2.1, 2.9) 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*: - -1.1% + 2.7%. - 1.14 + 2.7x3 - 1.6x, - 1.9x2 - -3.36 1.94, + 4.5x, - 12.03 #include #include using namespace std; #definen 3 Il number of unknowns Int main() 1 char quit Int!..k double an] - ((1.7.-1.1, 2.7).(-1.1, 1.6 -1.93. (2.7.-1.9.4.53 double b[n) - 17.39, -3.36, 12.03); // right hand side constant vector double xn! double nin). Yn). sum: //--................... Processing Section - // Formation of Land U as factors of A. I... A-LU for ( 0;len; I++ ) for (1-0:1++) 100] -0.0: COTO) - sart atoo)): for (1-1::-) 010) -as)[0]/ICO): for(i=1;i // Forward substitution phase for solving LY-B ( - )) YO) - b[0] / 0) for (-1; In: I++ ) { sum - 0.0 ; for (1-0-1-1; ++) sum-sum + 100 Yll: y[I] - ( i] - sum ) / ION : } // Back Substitution Phase for solving LT X=Y (* = [y: - Eyes: 1,2]) x[n-1] = y[n-1] /[[n-1][n-1]; for(i=n-2; i>=0; i--) { sum = 0.0 ; for(j=i+1; j> quit: return 0; }<><><><><><><><><><><><>