Math Help - Determinants of Large Matrices

1. Determinants of Large Matrices

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

2. 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.

Thanks!

3. 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?

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

4. 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.

Thanks!

5. 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.