Irregular system of equations

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I have a very basic elementry school question :-)

A system of linear equations as below:

$\big[\frac{1}{R} \mathbf{K} + \mathbf{S}\big] \mathbf{F}=\mathbf{RHS} $

in which $\mathbf{K}$ and $\mathbf{S}$ are $n \times n$ matrixes and $\mathbf{F}$ ($n\times 1$) and parameter $R$ are $n+1$ unknowns alltogether is given.

in addition to the equation above, we have another condition:

$M_i F_i =1$.

This system is $(n+1)\times(n+1)$ system of equation.

But I don't know how can I put all unknowns in a column vector, say $\bar{\mathbf{F}}$, and convert it to a system like:

$\bar{\mathbf{K}}\bar{\mathbf{F}}=\bar{\mathbf{RHS}}$

any solutions for numerical evaluation of it, using matlab, would also be helpful.

Thanks folks!