Let's denote the vectors in basis B1 as $v_1, v_2, v_3, v_4$ and the vectors in basis B2 as $w_1, w_2, w_3, w_4$. We can write the following equations:
$$w_1 = a_{11}v_1 + a_{21}v_2 + a_{31}v_3 + a_{41}v_4$$
$$w_2 = a_{12}v_1 + a_{22}v_2 + a_{32}v_3 +
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