- #1

Alex6200

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Question #1

## Homework Statement

Find a basis for the subspace of R3 for which the components in all of the vectors sum to zero.

## Homework Equations

If u and v are in w and w is a subspace, then a*u + b*v is in w.

## The Attempt at a Solution

w = {v in R3 : v1 + v2 + v3 = 0}

Okay, so let's say you have Ax = b, where the column space of A is the basis B, and b is a vector which is in w.

I really don't know how to work with this problem beyond that. I can imagine a basis looking something like:

[1, 0, 0], [0, -1/2, 0], [0, 0, 1/2]

Because if you add those vectors together, all of the components sum to 0. And those are indeed linearly independent. But I don't know if those are the right basis vectors.

Thanks,

Al.