Orthogonal basis

[LuisCMartins]

Consider the Subspace on R3:

U={(x1,x2,x3) € R3: x1 -2x2 +x3 =0}

Which of the following group of vectors is an orthogonal basis of U?

A - {(1,-2,1), (-1,0,1)}
B - {(-1,0,1), (1,1,1)}
C - {(2,1,0), (-1,0,1)}
D - {2,1,0), (0,0,1)}
E - {(1,-2,1), (-1,0,1), (1,1,1)}

Can anyone give me a detailed resolution of this? I tried to solve this several times but I have no idea how to do this since all of my orthogonal basis problems have a diferent structure than this one, so I don't really know how to start. I need an answer as soon as possible since I'm having an exam this week.

 

[Deleted member 4993]

Consider the Subspace on R3:

U={(x1,x2,x3) € R3: x1 -2x2 +x3 =0}

Which of the following group of vectors is an orthogonal basis of U?

A - {(1,-2,1), (-1,0,1)}
B - {(-1,0,1), (1,1,1)}
C - {(2,1,0), (-1,0,1)}
D - {2,1,0), (0,0,1)}
E - {(1,-2,1), (-1,0,1), (1,1,1)}

Can anyone give me a detailed resolution of this? I tried to solve this several times but I have no idea how to do this since all of my orthogonal basis problems have a diferent structure than this one, so I don't really know how to start. I need an answer as soon as possible since I'm having an exam this week.

C is not orthogonal - now you are left with choice from A, B, D or E.

Go to:

http://tutorial.math.lamar.edu/Classes/ ... Basis.aspx

In particular study (and apply) theorem 2.

Please share your work with us, indicating exactly where you are stuck - so that we know where to begin to help you.