# Determine wether 'u' is orthogonal to span(w)

• Nov 24th 2010, 07:47 PM
l flipboi l
Determine wether 'u' is orthogonal to span(w)
Hello,

can someone help me get started on this?

How can i show that u = (-1,1,0,2) is orthogonal to the subspace spanned by the vectors w1=(0,0,0,0) w2=(1,-1,3,0) w3=(4,0,9,2)

how would I set this up..

Thanks!
• Nov 24th 2010, 09:17 PM
math2009
$<\vec{u}~,~\vec{w}_i>=0$
• Nov 25th 2010, 03:28 AM
HallsofIvy
That is, a vector $\vec{u}$ is orthogonal to the span of a set of vectors if and only if it is orthogonal to each vector in the set.