- #1
daniel123244
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Homework Statement
Basically I am trying to find a spanning set for the plane through the origin with a normal of
(3,-2,1) that is an element of R3
"Let u = (3, 2, 1), and U ={wεR|w*u=0}"
Find a spanning set for U
2. The attempt at a solution
Just guessing blindly here:
(3,-2,1)=3(1,0,0)-2(0,1,0)+1(0,0,1)
we were taught to say (1,0,0)=e1, (0,1,0)=e2, and (0,0,1)=e3 so:
3e1-2e2+e3 would be a linear combination of this vector (?)
then if I let:
v=(x,y,z)=x(1,0,0)+y(0,1,0)+z(0,0,1)
u(dot)v=3xe1-2ye2+ze3=0
so does U=span{3xe1,-2ye2,ze3} ? I just don't know how to account for the fact that they equal 0 in the span.
Thank you to anyone who can help!