Question

This is a tricky one. Find the determinant of the following matrix.

Answer 1

I am not sure how to remove the alpha and beta but I know I have to use row operations. Any assistance would be appreciated :)

Answer 2

You know for a fact that you're removing alpha and beta and that the determinant isn't just a function of these?

Answer 3

This is the question:
Calculate the determinant of the following matrix. (Remember to use row and column operations to reduce the amount of cofactor expansion needed. The entries and should disappear early in the process.)

Answer 4

can you make a row or column into zeros? that would make it easier

Answer 5

I have made an entire column into zero with 1 as the pivot. I am trying to get it into row echelon format.

Answer 6

Remember, \[\det(A)=\det(A^T)\] so you can add rows to rows just like you can add columns to columns.

Don't bother trying to get it into row echelon format. Once you have a column or row with all zeroes except for one number, then you can take that one number and multiply it by the determinant of the matrix (n-1)x(n-1) left by removing the column and row shared by that single number.

Answer 7

For instance, adding the second column to the last column allows you to have 2*det(smaller matrix)

And what do you know, beta is gone! =)

Answer 8

Called a laplace reduction

Answer 9

Ok, so I have reduced to this so far after a few row operations