vector x which is the solution of the linear system 2*a*(x+b)=c-b in matlab

To solve the linear system 2a(x+b)=c-b in MATLAB, we need to isolate the variable x. Let's first simplify the equation by multiplying both sides by the inverse of 2*a, which gives:

x + b = (c - b) / (2 * a)

We can further simplify this by subtracting b from both sides:

x = (c - b) / (2 * a) - b

Now we can create a MATLAB code to find the solution vector x:

main.m
a = [1 2; 3 4];   % example values for a, b, and c
b = [5; 6];
c = [7; 8];

x = (c - b) ./ (2 * a) - b
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The output will be a 2x1 vector x containing the solution to the linear system. Note that the division operator used here is element-wise division, denoted by ./.