Answer:
Check the explanation
Step-by-step explanation:
MATLAB Code:
close all
clear
clc
% Part (a)
format rat
A = [-3 -2 4; -6 4 12; 6 -8 -11]
% Note: For Elementary Row Operation: Ri <- Ri + b*Rj
% E = eye(size(A)); E(i,j) = b;
% Elementary Row Operation: R2 <- R2 - 2*R1
E1 = eye(size(A)); E1(2,1) = -2
% Elementary Row Operation: R3 <- R3 + 2*R1
E2 = eye(size(A)); E2(3,1) = 2
E2E1A = E2*E1*A
% Elementary Row Operation: R3 <- R3 + (12/8)*R2
E3 = eye(size(A)); E3(3,2) = 12/8
U = E3*E2*E1*A
% Part (b)
L = inv(E1)*inv(E2)*inv(E3)
fprintf('Hence, L is a lower triangular matrix with ones on the diagonal.\n\n')
format short
A_LU = A - L*U;
disp('A - LU ='), disp(A_LU)
fprintf('Hence, A = LU.\n')
Kindly check the image below to see the Output.
