00:01
To use cramer's rule, we'll start by putting these equations into a matrix.
00:04
So the first column will correspond to x, the second to y, and the third to z.
00:08
And to fill in the matrix, we will use the coefficients that are in these equations.
00:13
Okay, so let's start with the first equation.
00:18
We have 8x minus 7y plus 1z.
00:24
In the next equation, we have minus 1x plus 5y minus 5z.
00:29
And in the last equation, we have 6x plus 1y plus 1z.
00:35
Okay, now to use cramer's rule, we'll need to use the determinant of this matrix.
00:39
So i'll let d be the determinant.
00:41
Now let's calculate that.
00:43
We have 8 times 5 times 1, which is 5 minus 1 times negative 5.
00:51
So that's minus negative 5, which is plus 5.
00:54
And then we have minus negative 7 multiplied by negative 1 times 1, which is negative 1, minus 6 times negative 5, which is negative 30.
01:07
So we have plus 30.
01:08
And then finally, we have plus 1 multiplied by negative 1 times 1, which is negative 1, minus 6 times 5, which is 30.
01:20
Okay, so let's simplify this.
01:22
We have 8 times 10 plus 7 times 29 plus negative 31.
01:34
Okay, so this is 80 plus 203 minus 31, which is 252.
01:46
Okay, now we'll need to define a new matrix.
01:49
The first column will correspond to the right -hand side of these equations.
01:53
The second will correspond to y, and the third will correspond to z.
01:57
Okay, so we have negative 43, negative 7, 1.
02:01
Okay, these columns will be unchanged.
02:06
So we can just copy those over.
02:09
Okay, and then the other right -hand side are 35 and 5.
02:18
Okay, and we'll need to take the determinant of this matrix.
02:21
So i'll make some space.
02:23
We will call the determinant of this matrix d sub x.
02:27
Okay, so let's calculate that.
02:29
We have negative 43 times 5 times 1, which is 5 minus 1 times negative 5.
02:37
So that is plus 5.
02:39
And next we have minus negative 7.
02:42
Okay, times 35 times 1, which is 35 minus 5 times negative 5.
02:48
So that's plus 25 plus 1 multiplied by 35 times 1, which is 35 minus 5 times 5, which is 25.
03:01
Okay, let's simplify this...