Use linear algebra methods to solve the following system of...

Use linear algebra methods to solve the following system of algebraic equations x + 2y + 3z = 2 2x + y + 3z = 0 3x + 2y + z = 3 You can use software to perform matrix operations, as long as it is clear from your work that you know what you are doing (i.e. you cannot just plug the system into software to obtain the answer I am seeking).

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00:01 Here we have a system of linear equations and we're going to solve them with an augmented matrix.

00:05 So let's jump right in, make our matrix.

00:09 Column 1 is our x variable.

00:11 Volume 2 can be y, column 3 can be z, and the final column is the right -hand side.

00:25 Here's our matrix.

00:27 And now what we're going to do is first turn this 3 here.

00:34 Into a 1 and i'm going to do that by taking row 3 away from it.

00:41 So i'll have row 1 minus row 3, which is just easier for elimination later on.

00:49 So row 2 and 3 are untouched by this.

00:53 I'll fill those back in.

00:58 Row 1, this is now a 1, minus 1, 5, minus 3.

01:15 Now we can perform elimination.

01:16 On this column.

01:19 So we're going to have minus 4, row 1, added to row 2, to eliminate that 4, and minus 2, row 1 added to row 3, to eliminate about 2.

01:37 So now row 1 is going to stay the same, row 2.

01:43 Okay, so we've got 0, minus 5, minus 4, minus 1 we've got 7 minus 20 so we've got 13 and we've got 1 minus 12 we've got 13 and now for row 3 this 2 is eliminated 3 2 is 5 minus 2 minus 10 and 6 plus 6 to 12.

02:30 Like so.

02:32 Okay...

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