2x + 3y − z = 5 −2y + 4x + 3z = 10 y + z + x = 3 2z + 3x − y = 8 in this overdetermined case the solution is not exact but rather a least-squares solution. calculate the residual sum of squares. in matlab

To calculate the residual sum of squares in MATLAB for the given system of equations, we can use the lscov function.

First, we need to define the matrices A and b representing the coefficients and the RHS of the linear equations, respectively. The system of equations can be represented as Ax = b.

main.m
A = [2, 3, -1; 4, -2, 3; 1, 1, 1; 3, 3, -1];
b = [5; 10; 3; 8];
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Next, we need to use the lscov function to calculate the least-squares solution x and the residuals.

main.m
x = lscov(A, b);
residuals = norm(A * x - b)^2;
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Finally, we can calculate the residual sum of squares by taking the squared norm of the residuals.

main.m
residual_sum_of_squares = sum(residuals);
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So, the MATLAB code to calculate the residual sum of squares for the given overdetermined system of equations is:

main.m
A = [2, 3, -1; 4, -2, 3; 1, 1, 1; 3, 3, -1];
b = [5; 10; 3; 8];
x = lscov(A, b);
residuals = norm(A * x - b)^2;
residual_sum_of_squares = sum(residuals);
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The residual_sum_of_squares will contain the residual sum of squares for the given system of equations.