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

You can solve the linear system 2a(x+b)=c-b in Matlab using the backslash operator ().

Assuming that variables a, b, and c are already defined, we can write the following code to solve the linear system and obtain the vector x:

main.m
x = (c - b) / (2 * a) - b;
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This code calculates the right-hand side of the equation (c-b)/(2a) and subtracts b from the result to obtain the solution vector x.

Note that in Matlab, the backslash operator () can also be used to solve linear systems by writing them in the form Ax = b, where A is the matrix of coefficients, b is the right-hand side vector, and x is the solution vector. In this case, we have:

main.m
2*a*x + 2*a*b = c - b

2*a*x = c - b - 2*a*b

x = (c - b) / (2 * a) - b
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So we can directly apply the backslash operator:

main.m
x = 2*a \ (c - b - 2*a*b);
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Both approaches give the same solution for vector x.