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(Step-by-Step) Simultaneous left inverse. The two matrices

Question: Simultaneous left inverse. The two matrices

\[A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 1 \\ 2 & 1 \\ 2 & 2 \end{array}\right], \quad B=\left[\begin{array}{ll} 3 & 2 \\ 1 & 0 \\ 2 & 1 \\ 1 & 3 \end{array}\right]\]

are both left-invertible, and have multiple left inverses. Do they have a common left inverse? Explain how to find a \(2 \times 4\) matrix \(C\) that satisfies \(C A=C B=I\). Please write down your approach here, but not the matrix \(C\) explicitly. You will solve for \(C\) in the Julia portion of this homework.

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