The matrix obtained by the product of two orthogonal vectors from two different spaces

Question

Let them be $${u_1,u_2,u_3,u_4}$$ and $${v_1,v_2,v_3,v_4,v_5,v_6}$$ orthonormal vectors in $\mathbb{R}^4$ and $\mathbb{R}^6$ , and $$A=v_1u_1^{T} + v_2u_2^{T}$$

How to determine the solution system $$Ax=2v_1+v_2$$

Answer 1

HINT: What if you look at all vectors $x\in\Bbb R^4$ with $x\cdot u_1 = 2x\cdot u_2$? (To solve this, you can rewrite the equation in homogeneous form easily enough.) Note, in particular, that any vector in the span of $u_3$ and $u_4$ automatically satisfies the equation.