00:01
So in this problem, we're given these three linear equations, and we're asked to use gaussian elimination to solve this with.
00:19
So that means first we need to write the augmented matrix.
00:23
So we take the coefficients on the left -hand side, 4 -1 minus 1, and in the fourth column we will put the constant from the right -hand side.
00:34
So the next row, 5, 1, 2, 4, 6, 1, 1.
00:41
One six and now we solve this through row reduction efforts okay well what can we see how about if we take take row two minus row one and row three minus row one what i will do is eliminate those two entries right off the bat here for us so row one stays four one minus minus 1, minus 2.
01:25
So then 4 minus 5 is 1, 0, 1 minus 1.
01:31
2, minus a minus, that's plus 1, that's 3.
01:35
And then 4 minus a minus, that's plus.
01:38
So 4 plus 2 is 6.
01:42
And then 4, let's see, 6 minus 4 is 2, 0 there, of course.
01:50
1 minus a minus, that's plus.
01:52
So 1 plus 1 plus 1 is 2.
01:55
And six minus minus plus two.
02:00
Six plus two is eight.
02:03
Okay.
02:04
Now, we have a one here in the first entry, don't we, in the second row? so let's use it to eliminate these two entries.
02:20
So i'll do row one minus four times row two, and row three minus two times row two.
02:31
Okay.
02:32
So row 2 is going to be unchanged as such.
02:40
So row 1, i'll have a 0 here because 1, i'll see 4, minus 4 is 0, and i'll have a 1 there, and then i'll have minus 1, minus 1, minus, or see, minus 4 times 3, so that's minus 12.
02:58
So it's minus 1, minus 12, that's minus 13.
03:02
And then i'll have minus 2, minus 4 times 6 is 25.
03:07
So that's minus 26.
03:13
Okay.
03:14
Row 3.
03:15
Again, i'll have a 0 here, a 0 here...
