standard model - How does a Higgs triplet transform under $SU(2)_L times U(1)_Y$ when written as a $2times 2$ matrix?

I recently learned that a Higgs triplet can be written as a $2 \times 2$ matrix:

$$\begin{equation} \Delta=\begin{pmatrix} \frac{\Delta^{+}}{\sqrt{2}} & \Delta^{++} \\ \Delta^0 & - \frac{\Delta^{+}}{\sqrt{2}}\end{pmatrix} \end{equation}$$

Typically, an $SU(2)$ triplet $\phi$ transform like:

$$\begin{equation} \phi \rightarrow\exp(-i\vec{T}\cdot \vec{\theta})\phi \end{equation}$$

where $\vec{T}$ are some $3\times3$ matrix representation of the $SU(2)$ generators. How to modify the $\vec{T}$'s such that $\Delta$ transform like a triplet under $SU(2)_L$?