Thread: Determinants of Large Matrices

How would I find the the determinants of the following matrices without using my calculator? Is there a fast way?

Thanks in advance!

Um, I was asking about *determinants.* Unless determinants are the same as dimensions, but I don't think that your post found the determinant of either matrix.

Could someone please help me with determinants?

Thanks!

Hello,

Originally Posted by Winding Function

How would I find the the determinants of the following matrices without using my calculator? Is there a fast way?

Thanks in advance!

The determinant of a matrix nxn is 0 iff the rank of the matrix is < n.
If two columns or rows of a matrix nxn are linearly dependent, then the matrix is not of rank n.

For the first one, the 4th column is 11 times the 1st one.
For the second one, it is obvious that with the null column, the matrix is not of rank n.


Edit : excuse me, I confused myself between rank and dimension

Um, I was asking about *determinants.* Unless determinants are the same as rank, but I don't think that your post found the determinant of either matrix.

Could someone please help me with determinants?

Thanks!

Originally Posted by Winding Function

Um, I was asking about *determinants.* Unless determinants are the same as rank, but I don't think that your post found the determinant of either matrix.

Could someone please help me with determinants?

Thanks!

The determinant of a matrix nxn is 0 iff the rank of the matrix is < n.

See the relationship ?

By the way, both answers are 0.