Consider the following two matrices

A $=$

$$

$$

$$

$$

$102$

$111$

$010$

$203$

$$

$$

$$

$$ and B $=$

$$

$$

$$

$$

$101$

$221$

$350$

$416$

$$

$$

$$

$.$

Determine the set of all vectors which belong to both Col$($A$)$ and Col$($B$).$ Express this set as a

span of linearly independent vectors. Provide evidence that you tested that your answer is correct.

For example, if you claim that a specific vector v in R$4$ is in Col$($A$)$ and in Col$($B$),$ then provide

a specific vector x in R$3$ such that Ax $=$ v and a specific vector y in R$3$ such that By $=$ v