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Spencer

• How does this change the determinant of the Matrix?

If I have the matrix (M) with the determinant det(M), and then i have the matrix M' which is:

[            |0,0]

[   M      |0,0]

[            |0,0]

[0, 0, t-1|,-1,0]

[0, 0, t-1|,-1,t]

would you have to take into consideration the [t-1]s? since they are directly "under" the M matrix. I put this into my calculator using placeholder numbers, and I got the determinant of M to be 9, and M' to be -9, when i substituted a -1 diagonally across from the original M matrix, even though I also added terms below the matrix. So although I'm confident that it doesn't change the determinant, I'm wondering WHY it doesn't.