C1_W3_Lab3 Liner tranformatio

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

In the first line, L is defined as a generic transformation where a matrix A with dimensions mxn takes any vector v mx1 to a different dimension nx1 through multiplication. After that, it is proposed a less challenging exercise where L is a transformation of R2 to R3. Hope this helps. Good luck mate.