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theRukus
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Homework Statement
Let U be a subspace of R4 and let S={x1, x2, x3} be an orthogonal basis of U.
Given x1, x2, x3, find a basis for Uperp (the subspace containing all vectors orthogonal to all vectors in U).
I am actually given three vectors x1, x2, x3, but I am looking more to understand the concept.
Homework Equations
The Attempt at a Solution
Since all vectors in Uperp are orthogonal all vectors in U, I am led to believe that all vectors in a basis of Uperp would be orthogonal to the vectors in the basis of U... But the vectors I am given are all orthogonal to one another, so I am somewhat confused.
Any insight is appreciated. Thank you.