00:01
In this problem, we're given a square matrix, and our job is to find the determinant of that matrix by using co -factor expansion in two ways, along the third row, and then along the first column.
00:12
So to set up the expansion along the third row, we've copied the matrix over.
00:18
Here's the third row.
00:20
So that co -factor expansion looks like this.
00:23
We use this notation for the determinant of m.
00:26
So we take two in the third row first column.
00:30
We eliminate those and take the determinant of the remaining matrix, which is the matrix 2321.
00:39
Then we're going to alternate signs.
00:40
So we have minus three, the element in the third row second column.
00:45
We eliminate those rows and columns.
00:48
The resulting matrix is this.
00:50
We'll need to take its determinant.
00:53
And finally, we will take the element in the third row, third column.
00:57
Apply the same idea...