Construct a 2 by 3 system that has these particular and homogeneous eq

[s3a]

Homework Statement

Construct a 2 by 3 system Ax = b with particular solution x_p = (2,4,0) and homogeneous solution x_n = any multiple of (1,1,1).

The answer is {{1,0,-1},{0,1,-1}} x = {{2},{4}} which has x_p and x_null = (c,c,c).

Homework Equations

Ax = b

The Attempt at a Solution

I tried putting (2,4,0) as row 1 and (1,1,1) as row 2 and then reducing, I get {{1,0,2},{0,1,-1}} but, that doesn't seem to match up with the answer.

Could someone please tell me how to do such a problem?

Any input would be greatly appreciated!

 

[mfb]

Similar to solving those problems, it is useful to begin with the homogeneous solution. The particular solution can be added afterwards.

The answer is

One possible answer.