use lu decomposition to fi nd a solution to the system: x + 7y − 9z = 12 2x − y + 4z = 16 x + y − 7z = 16 in matlab

Here is how to use LU decomposition to find the solution of the given system in MATLAB:

main.m
% Define the coefficient matrix and the constant vector 
A = [1, 7, -9; 2, -1, 4; 1, 1, -7];
B = [12; 16; 16];

% Find the LU decomposition of A
[L,U,P] = lu(A);

% Solve for y in Ly = PB
y = L \ (P*B);

% Solve for x in Ux = y
x = U \ y;

% Display the solution vector x
disp(x);
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In the above code, we first define the coefficient matrix A and the constant vector B. Then, we use the lu function to find the LU decomposition of A. The function returns three matrices L, U and P such that PA = LU.

Next, we solve for y in the equation Ly = PB using the left division operator \. Then, we solve for x in the equation Ux = y using the same operator. Finally, we display the solution vector x using the disp function.

Note that the LU decomposition method is not always the most efficient, so depending on the specific problem, other methods may be preferred.