Solving system of equations for matrix?

[mneox]

Homework Statement

Solve the system of equations for Bx = 0.

Where B is the following matrix:
[ 5 -1 ]
[ 2 2 ]
[ 1 4 ]

and the x is some vector I am assuming.. is it:
[ x1 ]
[ x2 ]

Homework Equations

The Attempt at a Solution

So what I figured was that I should do this:

[ 5 -1 | 0 ]
[ 2 2 | 0 ]
[ 1 4 | 0 ]

Is this correct? Then if I get it to rref

[ 1 0 | 0 ]
[ 0 1 | 0 ]
[ 0 0 | 0 ]

What do I do now? Is x₁ = 0 and x₂ = 0?

That seems like it's incorrect so I was wondering if someone can check over for me and offer any help? Thank you! :)

 

[Mark44]

Why do you think it's incorrect? You can check your work, you know. What do you get when you multiply
$$\left[\begin{array}{c c}5&-1\\2&2\\1&4\end{array}\right]<br /> \left[\begin{array}{c}0\\0\end{array}\right]$$
What should you get?

 

[mneox]

Why do you think it's incorrect? You can check your work, you know. What do you get when you multiply
$$\left[\begin{array}{c c}5&-1\\2&2\\1&4\end{array}\right]<br /> \left[\begin{array}{c}0\\0\end{array}\right]$$
What should you get?

Won't that give me a zero matrix? How would that help solve the system??
Sorry if I'm asking such stupid questions but it's been a long week..

 

[HallsofIvy]

The problem was to find an x such that Bx= 0. You have found that x= (0, 0) is the only such x. What is wrong with that?