Problem in setting homogenous parameters

[shellizle]

Homework Statement

how to put x+z=0, and y-z+2w=0 into matrices in terms of two parameters?

Homework Equations

AX=0, looking for x

The Attempt at a Solution

x=-z
y=z-2w

(-1, 1, 1, 0)z, no idea what the other matrix is :S

thanks advance guys!

 

[Mark44]

Your question is somewhat misleading. I don't think you want to put the equations into matrices, but rather find two vectors that are a basis for the nullspace (or kernel) of your matrix A.

You can write z and w in terms of x and y, like so:
z = -x
w= -.5x -.5y
In the latter equation, I substituted -x for z in the equation y -z + 2w=0.


x=1x+0y
y=0x+1y
z=-1x+0y
w=-.5x-.5y

So in the equations above, a vector x = (x, y, z, w) can be written as a linear combination of two other vectors.