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?



Cotangent bundle
$$
0 \to O(-3) \to O(-2)^{\oplus 3} \to \Omega^1 \to 0.
$$


