If
for every

, then the columns of
are linearly independent.

Question

If 
  for every 
  
, then the columns of 
  are linearly independent.

Quizplus · Accepted Answer

Since the only difference between the two given strings is in the fourth group of characters, which implies that the value in this group doesn't affect the output. Therefore, the columns of the second string would be the same as the columns of the first string, and since they are linearly independent, the columns of the third string would also be linearly independent.

If for Every