00:01
I'm going to solve this system of linear equations using an augmented matrix.
00:06
Okay so the first column of the matrix will correspond to x, the second to y, and the third to z.
00:13
Okay so we'll use these coefficients to fill in the matrix.
00:17
So we have 3x minus 4y plus 2z equals negative 20.
00:23
And then in the second equation we have 2x plus 4y plus 1z equals 19.
00:29
And finally in the third equation we have 2x plus 3y plus 5z equals 26.
00:40
Okay so this is our augmented matrix.
00:45
I'm going to use elementary row operations in order to reduce it.
00:51
So the first operation is row 1 plus row 2 to get the new row 1.
01:00
Okay so we have 3 plus 2 is 5, negative 4 plus 4 is 0, 2 plus 1 is 3, and negative 20 plus 19 is negative 1.
01:11
Next i'll take row 3 and subtract row 2 to get the new row 3.
01:18
Okay so we have 2 minus 2 is 0, 3 minus 4 is negative 1, 5 minus 1 is 4, and 26 minus 19 is 7.
01:30
I'm sorry i realized i made a mistake here.
01:32
It should be row 3 minus row 2.
01:36
Okay so i did 2 minus 2 to get 0, 3 minus 4 to get negative 1, 5 minus 1 to get 4, and 26 minus 19 to get 7.
01:51
So sorry about that.
01:53
Okay finally i'm going to take row 2 and add it to 4 times the new row 3.
02:02
Okay to get the new row 2.
02:05
So we have 2 plus 0 is 2, 4 minus 4 is 0, 1 plus 16 is 17, and 19 plus 28 is 47.
02:24
Okay so here is the reduced matrix.
02:28
We're still going to reduce it a little more.
02:32
So i'm going to take 2 fifths of row 1 and add it to row 2 to get the new row 1...