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Let U be a proper subspace of R^4 and let it be given by the equations:

1) x1+x2+x3+x4=0

2) x1-x2+2x3+x4=0

how do i find a basis for this subspace???

I got that (0,1,2,0) is one of the basis vectors since x2=2x3, therefore whatever we pick for x2, x3 will be twice that value.

i also got that x4=-x1-1.5x3, but does this require two more basis vectors or one?

ie, i'm asking, it seems that every x value can be determined once x1 and x2 are determined, therefore it should have 2 basis vectors, but i cant quite put it into that form

1) x1+x2+x3+x4=0

2) x1-x2+2x3+x4=0

how do i find a basis for this subspace???

I got that (0,1,2,0) is one of the basis vectors since x2=2x3, therefore whatever we pick for x2, x3 will be twice that value.

i also got that x4=-x1-1.5x3, but does this require two more basis vectors or one?

ie, i'm asking, it seems that every x value can be determined once x1 and x2 are determined, therefore it should have 2 basis vectors, but i cant quite put it into that form

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