We have the sequence $0 \rightarrow \Omega^1_{\mathbb{P}^2}\rightarrow3\mathcal{O}_{\mathbb{P}^2}(-1)\rightarrow \mathcal{O}_{\mathbb{P}^2}\rightarrow 0$.

Can we write a exact sequece such that $\Omega^1_{\mathbb{P}^2}$ is on the right?

We have the sequence $0 \rightarrow \Omega^1_{\mathbb{P}^2}\rightarrow3\mathcal{O}_{\mathbb{P}^2}(-1)\rightarrow \mathcal{O}_{\mathbb{P}^2}\rightarrow 0$.

Can we write a exact sequece such that $\Omega^1_{\mathbb{P}^2}$ is on the right?

Sorry if the question was not properly written, I'm looking for a exact sequece of the form $0 \leftarrow \Omega^1_{\mathbb{P}^2}\leftarrow \bigoplus\mathcal{O}_{\mathbb{P}^2}(a_{1i})\leftarrow \bigoplus \mathcal{O}_{\mathbb{P}^2}(a_{2i})\leftarrow \cdots$ (with all the terms given by sums of line bundles)

If it exists how can I contruct it?