In fact, it should be (with –1s on the subdiagonal).

Using row and column operations, add t times the first column to the second column, then t times the (new) second column to the third column, and so on until you add t times the (n-1)th column to the n'th column. That kills off all the t's on the main diagonal (except for the first one), and you are left with . Now expand down the last column.