(Solved): Find a \( 2 \times 3 \) matrix \( A \) and a vector \( \vec{b} \) such that general solution of \( ...

Find a \( 2 \times 3 \) matrix \( A \) and a vector \( \vec{b} \) such that general solution of \( A \vec{v}=\vec{b} \) is \[ \vec{v}=\left[\begin{array}{c} 4 \\ -1 \\ 0 \end{array}\right]+t\left[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}\right] \]