00:01
So for this question we will be using the method of augmented matrix.
00:05
So this is 2, 2, 2 and this is 0.
00:10
So i'm just writing the coefficients of x1, x2 and x3 over here.
00:16
And in the right most, in the right most column, what i'll do is i'll just write the values of the equalities of those equations.
00:27
Okay so now try to make this zero and this zero and after that make this zero using this so first transformation is r2 goes to r2 minus r2 plus r1 and r3 goes to r3 minus four times of r1 so now what we will have is this is two two and this is zero this will be 0 now just add these two so this is 7 and this is 4 and this is 1 right r3 minus 4 r1 this is 0 minus 4 so this is minus 7 right and then 4 minus 8 so that will be how much minus 4 and this is minus 1 correct now add these 2 okay so this is 2 2, 2 ,0, 0, 0, 7, 4, 1.
01:43
0, 0 and 0.
01:46
Oh, interesting.
01:48
So this says that 0 times of x plus 0 times of y plus 0 times of z equals to 0.
01:58
I mean, in the question, it's given x1, x2, x3.
02:02
So just let me use x1 x2 .3 only.
02:04
X 1 x0 times of x2 0 times of x3 is equal to 0 so this equation is always satisfied for any x1 x2 and x3 we don't need to worry about this just worry about these two equations so one says 7x2 plus 4 x3 is equal to how much 1 and this one says x1 plus x2 plus x3 is equal to 0 right so from these two equations what you will get? you will be getting a range.
02:43
You will be getting some general values.
02:46
You can't get the exact value because there are two equations but we have three variables.
02:53
So you will be getting a range.
02:56
So anything you can do, you just eliminate x3, multiply this equation with 4 and subtract it.
03:07
Right...
