WEBVTT
00:00:00.520 --> 00:00:13.680
Find the value of the determinant of the matrix eight, negative two, six, negative nine plus the determinant of the matrix three, negative 11, negative 15, six.
00:00:14.760 --> 00:00:19.720
The first thing we can see is that both of our matrices are two by two.
00:00:20.680 --> 00:00:26.840
And actually, to find the determinant of a two-by-two matrix, we have a particular rule.
00:00:27.480 --> 00:00:42.120
And this rule tells us that the determinant of a two-by-two matrix in the form ๐๐๐๐ is equal to ๐ multiplied by ๐ minus ๐ multiplied by ๐.
00:00:43.280 --> 00:00:44.640
Okay, great!
00:00:45.160 --> 00:00:46.680
So now we have this rule.
00:00:47.320 --> 00:00:50.040
We can actually use it to help us solve the problem we have.
00:00:50.880 --> 00:00:52.120
So now we have our sum.
00:00:52.600 --> 00:00:57.760
And what we need to do is actually work out the value of each determinant and then add them together.
00:00:58.720 --> 00:01:02.880
So first of all, weโre gonna have eight multiplied by negative nine.
00:01:03.640 --> 00:01:05.720
And thatโs because thatโs like our ๐ and our ๐.
00:01:06.440 --> 00:01:08.120
And then this is gonna be minus.
00:01:08.800 --> 00:01:11.800
Then weโve got negative two multiplied by six.
00:01:12.880 --> 00:01:16.720
And thatโs because this is our ๐ and our ๐ in our determinant.
00:01:17.800 --> 00:01:19.120
Okay, great!
00:01:19.720 --> 00:01:23.000
So thatโs our first determinant taken care of.
00:01:24.000 --> 00:01:25.800
Now letโs have a look at the second determinant.
00:01:26.120 --> 00:01:33.360
Well, weโre gonna be dealing with three multiplied by six because again this is our ๐ and our ๐.
00:01:34.200 --> 00:01:38.280
And then weโre gonna subtract negative 11 multiplied by negative 15.
00:01:39.080 --> 00:01:41.720
This is because this is our ๐ and our ๐.
00:01:42.760 --> 00:01:44.120
Okay, great!
00:01:44.640 --> 00:01:45.960
So now weโve got both our determinants.
00:01:46.640 --> 00:01:49.400
What we need to do is actually figure out what the value of each of them is.
00:01:50.200 --> 00:01:55.280
Okay, so our first determinant is gonna be equal to negative 72 plus 12.
00:01:56.480 --> 00:02:08.600
And then this is gonna be added to our second determinant, which is 18 minus 165, which is gonna be equal to negative 60 plus negative 147.
00:02:09.840 --> 00:02:18.600
So therefore, itโs gonna be the same as negative 60 minus 147, which gives us an answer of negative 207.
00:02:19.400 --> 00:02:38.880
So therefore, we can say that the value of the determinant of the matrix eight, negative two, six, negative nine plus the determinant of the matrix three, negative 11, negative 15, six is gonna be equal to negative 207.