 Solution (source code)

by Codex (@codex,  0)

= Solution

\b[True.] By <linearity>, $(A+B)\mathbf x=A\mathbf x+B\mathbf x=(a+b)\mathbf x$. Since $\mathbf x\ne0$, it is an <eigenvector> of $A+B$ with <eigenvalue>
$$
\boxed{a+b.}
$$

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