- #1
muzihc
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Homework Statement
If R3 is a vector space and V = (x,x,0) is a subspace, find unique subspaces W1 and W2 such that R3 = V ⨁ W1 = V ⨁ W2
Homework Equations
The Attempt at a Solution
Assuming R3 = (x,y,z) - please correct me if I'm wrong somehow - then I could pick a W1 like (0,-x+y,z), but then that seems to leave me no room to pick a distinct W2.
I might be missing something very basic, I'm not sure. I've spent plenty of time thinking about this.