00:02
So here we are asked to find the determinant of this 4x4 square matrix using expansion by cofactors.
00:11
So expansion by cofactors tells us that the determinant is a11 -1 -1, plus a12, c -12, plus a -13, c -1 -4, c -1 -4.
00:33
Because a12 is 0, we can neglect this portion because 0 times anything will be 0 automatically.
00:42
So let's move on.
00:45
So a11 is simply element in row 1, column 1.
00:49
So that's just 1.
00:50
C1 is the same as minor m11.
00:54
So we delete row 1, oh sorry, row 1 in column 1.
00:58
So we are left with 1, 01, 3, negative 1, 2, negative 1, negative.
01:03
Negative one, zero, one.
01:08
Then we move on to a13, so we have negative two, times c13, we delete this column.
01:16
So we have zero, zero, zero, one, three, negative one, one, two, one, plus a14, that's just one, times a negative of c -14 because 1 plus times the negative of m -14, sorry.
01:34
C -1 -4, the co -factor 1 -4, has an odd i -j because 1 plus 4 is 5, which is odd.
01:43
So c -1 -4 is the same thing as the negative of m -1 -4.
01:46
So we're finding m -1 -4, so we just negate it.
01:49
M -14, we delete row 1, column 4.
01:52
So we have 0 -0 -0 -1 -1 -3 -3 -9 -3 -9 -3 -9 -3 -9 -3 -3 -9 -6.
01:57
So negative 1, so negative 1.
02:00
So now we find the determinants of these 3 by 3 square matrices, again using a11, c11, plus a12, c13, c13.
02:12
So we have here, a11, so that's 1 times delete 4 1, column 1, negative 1, 0, 2, 2, 1.
02:27
And then we add a12, which is 0, so we can move on.
02:32
And then we add a13, which is 1, times c13.
02:37
So we delete row 1, column 3.
02:40
So we have 3, negative 1, negative 1, 0.
02:44
Now we move on over here.
02:46
So we have negative 2 times all of this.
02:51
So let's put brackets.
02:52
So a11 is 0.
02:55
So that means we can move on to a12, which is 1, times the negative of m12.
03:01
We delete row 1, column 2...