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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.

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# Homework Help: Find a basis

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