If
for a matrix

, and
is an onto linear transformation, then the number of columns of
is greater than or equal to the number of rows of

.

Question

If 
  for a matrix 
  
, and 
  is an onto linear transformation, then the number of columns of 
  is greater than or equal to the number of rows of 
  
.

Quizplus · Accepted Answer

Since the linear transformation is onto, it means that the range space of the matrix is equal to the codomain. Therefore, the number of columns of the matrix (which represents the dimension of the range space) should be greater than or equal to the number of rows (which represents the dimension of the domain).

If for a Matrix