# gauss jordan elimination (easy 10 points)?

use gauss jordan elimination to find the vector equation of the line of intersection of each pair of planes.

(i only need help setting the bottom x value, and top y value to 0)

4x - 8y - 3z = 6

-3x + 6y + z = -2

Relevance

So you have the following matrix:

4 -8 -3 6

-3 6 1 -2

I'll divide everything by 4, because I like to work with a 1 in the top corner. That gives:

1 -2 -3/4 6/4

-3 6 1 -2

Now multiply the top row by 3, add to the bottom row, and replace the bottom row:

1 -2 -3/4 6/4

0 0 -5/4 10/4

Let's multiply the bottom row by 4.

1 -2 -3/4 6/4

0 0 -5 10

And then let's divide by -5.

1 -2 -3/4 6/4

0 0 1 -2

Now, we multiply the bottom row by 3/4, add it to the top row, and replace the top row.

1 -2 0 0

0 0 1 -2

So now you're in reduced row echelon form.

• Add the first equation to (3 times the second equation) to obtain

-5x + 10y = 0; i.e. x=2y. Substituting back, we find z=-2. One way of writing the line of intersection is

{ (0, 0, -2) + t (2, 1, 0): t is real}.