wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Is the rank of a matrix equal to the rank of its transpose?


Open in App
Solution

Explaining why the rank of a matrix is equal to the rank of its transpose:

The rank of a matrix is always equal to the rank of its transpose because transpose is just converting a row into a column and vice versa. Therefore, the rank of the matrix does not change.

For example, let's consider a matrix

A=2626A=(6×2)-(6×2)=12-12=0

Since A=0, the rank is 1.

AT=2626AT=(6×2)-(6×2)=12-12=0

Since AT=0, the rank is 1

Therefore, the rank of a matrix equal to the rank of its transpose.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon