i dont understand this part guys like can anybody explain what he wants :

Let 𝐿:ℝ𝑚→ℝ𝑛

be defined by a matrix 𝐴

, where 𝐿(𝑣)=𝐴𝑣

, multiplication of the matrix 𝐴

( 𝑛×𝑚

) and vector 𝑣

( 𝑚×1

) resulting in the vector 𝑤

( 𝑛×1

).

Now try to guess, what should be the elements of matrix 𝐴

, corresponding to the transformation 𝐿:ℝ2→ℝ3

: