Homogeneous system of linear equation:

[TonyC]

I am having trouble finding the solution to the homogeneous system of linear equations:
2x-2y+z=0
-2x+y+z=0

 

[TonyC]

I guess I should have also put:

How can I break this down?

 

[FredGarvin]

Perhaps I have been out of the rigid math stuff for a while, but how are you going to solve a system with three unknowns and only two equations?

 

[TD]

Choose one variable (e.g. z) as "t" and solve the system for x and y in function of t.
You'll get an infinite number of solutions, for every t (so z), you have a couple (x,y).

 

[TonyC]

Hence my problem..
The answers to choose from are:
x=3/4t, y=-t,z=1/2t
x=-3/4t,y=-t,z=1/2t
z=-3/4t,y=t,z=1/2t
z=3/4t,y=t,z=1/2t

This is why I am stumped.

 

[TD]

In your case, y was substituted for t. Then solve it as if t was a parameter for x and z.

 

[TonyC]

? I am still confused.

 

[TD]

You start with

\left\{ \begin{gathered}<br /> 2x - 2y + z = 0 \hfill \\<br /> - 2x + y + z = 0 \hfill \\ <br /> \end{gathered} \right

Substitute y = t, t is now a parameter, and solve the following (2x2)-system for x and z

\left\{ \begin{gathered}<br /> 2x + z = 2t \hfill \\<br /> - 2x + z = - t \hfill \\ <br /> \end{gathered} \right

 

[HallsofIvy]

You might also want to review your list of possible answers. "x" got changed to "z" in some of them!

(Am I the only person who hates multiple choice questions in mathematics?)

 

[TD]

(Am I the only person who hates multiple choice questions in mathematics?)

(No )