1. Suppose v and u 6= 0 are vectors of the same dimension. Verify that v − proju(v) is
orthogonal to u.
Hint: Use the dot product!
Now let B =
be a set of three vectors in R
. We will modify this set of vectors to make it nicer in some respects.
2. Use the idea in 1 to modify the second vector in B to make it orthogonal to the
first vector in B.
3. Modify the third vector in B to make it orthogonal to both the first and second
vectors in B.
4. Modify the first vector in B and your modified vectors from 2 and 3 to have length one.
5. What might your final collection of modified vectors from 4 be good for ?
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