Mathematics II - Old Questions

19. Let V and W be the vector spaces over a field F of real numbers. Let dim V = n and dim W = m. Let {e₁,e₂,... ...,e_n} be a basis of V and {f₁, f₂, ... ... ... , f_m} be a basis of W. Then, prove that each linear transformation can be represented by an m x n matrix A with elements from F such that 

Y = AX

Are column matrices of coordinates of relative to its basis and coordinates of relative to its basis respectively.

OR

Compute the multiplication partitioned matrices for