00:01
So here we start with a system of equations that if we write this as an augmented matrix, we have 1, 1, 1, 1, 2, 4, negative 3, 1, 3, 6, negative 5, 0.
00:23
And using gaussian elimination to solve this system, let's see, if we reduce this, then i get 1, 1, 1, 1, take row 2, minus 2, row 1, and that's your new row 2, i have 2 minus 2 is 0, 4 minus 2 is 2, negative 3 minus 2 is negative 5, 1 minus 2 is negative 1, i take row 3, minus 3, row 1, that's my new row 3, so that is going to be 0, 6 minus 3 is 3, negative 5, minus 3 is negative 8, 0 minus 3 is negative 3.
01:09
Then let's take 1 half row 2 to be your new row 2, and row 3 minus 3 half row 2 to be your new row 3.
01:30
And then i get 1, 1, 1, 1, 0, 1, negative 5 halves minus 1 half.
01:44
Then 0 minus 0, 3 minus 3, negative 8 minus, let's see here, negative 8 minus 3 halves times negative 5, so this is negative 8 plus 15 over 2, that is negative 1 half, and then we have negative 3 minus 3 halves times negative 1.
02:19
So negative 3 plus 3 halves, which is negative 3 halves.
02:25
And then, let's see, we'll take row 3 to be negative 2, row 3, so 0, 0, 1, and 3.
02:45
Then we'll take row 2 to be row 2 plus 5, row 3.
02:54
And i get 0, 1, negative 5 halves plus 5 halves.
03:00
No, i want to subtract, sorry...