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|b\rangle\otimes|a\rangle \equiv \begin{bmatrix} b_0\begin{bmatrix}a_0\\a_1\end{bmatrix} \\ b_1\begin{bmatrix}a_0\\a_1\end{bmatrix}\end{bmatrix} = \begin{bmatrix}b_0a_0 \\ b_0a_1 \\ b_1a_0 \\ b_1a_1\end{bmatrix}.