If
for a matrix

, and
is a one-to-one linear transformation, then the number of columns of
is less than or equal to the number of rows of

.

Question

If 
  for a matrix 
  
, and 
  is a one-to-one linear transformation, then the number of columns of 
  is less than or equal to the number of rows of 
  
.

Quizplus · Accepted Answer

A one-to-one linear transformation preserves dimensionality, so the number of columns in the output matrix cannot be greater than the number of rows in the input matrix. Therefore, the number of columns of 11edaba5_20ad_ae31_a975_6f16a0d8db91_TBMC1039_00 is less than or equal to the number of rows of 11edaba5_20ad_ae32_a975_f94c71815e22_TBMC1039_00.

If for a Matrix