Using a orthonormal bases of $\mathbb R^4$ and $\mathbb R^6$ find a solution $Ax=z_1$
Let $q_1,q_2,q_3,q_4$ be orthonormal vectors in $\mathbb{R}^4$,$z_1,z_2,...,z_6$ orthonormal vectors in $\mathbb{R}^6$ and $A=z_1q_1^T + z_2q_2^T$.