Hi please can you help me in checking my work?(adsbygoogle = window.adsbygoogle || []).push({});

Find a basis for the following space of each of the following and specify its dimension.

2x_{1}+x_{2}-x_{3}+x_{4}=0

x_{2}+x_{3}-x_{4}=0

x_{2}+x_{4}=0

I found in solving the system that x_{4}can be an arbitrary and I let x_{4}=t

The solution is:

x_{1}=t

x_{2}=-t

x_{3}=2t

x_{4}=t

The dimension is one.

But I am confused about this one:

Find a basis for the following space of each of the following and specify its dimension

2x_{1}+x_{2}-x_{3}+x_{4}=0

Thank you for your help

B.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Find a basis

**Physics Forums | Science Articles, Homework Help, Discussion**