00:01
Okay, so we're given that every row of a tends to zero.
00:03
That is the sum of the entries in every row is zero.
00:06
We want to prove that the determinant of a is equal to zero.
00:09
So we do the row operations of adding all the remaining rows, so the first row of a transpose, and we get a matrix b consisting of all zeros in the first row.
00:18
And we know the addition or subtraction of the row to another row does not alter the value of the determinant.
00:23
Therefore, the determinant of a transpose is equal to the determinant of b, which is equal to zero.
00:28
And we know that the determinant of a is equal to the determinant of a transpose, so therefore the determinant of a is equal to zero.
00:36
Now we suppose that every row of a adds to 1.
00:39
So we write here, say, a minus i is equal to b given, here's our matrix b...