I have a linear transformation $f:\mathbb R^3\to \mathbb R^3$ and I have the matrix of that transformation in its base $(1, 0, 0)$, $(0, 1, 0)$, $(0, 0, 1)$.
\begin{bmatrix}
a & 1 & 1 \\
1 & b & 1 \\
1 & 2b & 1 \\
\end{bmatrix}

Now I need to find $a$ and $b$ such that the following is correct $(4, 3, 4)\in\operatorname{Im}(f)$.

I have tried some things, but it has led me nowhere. Could someone please give me an idea?