Maths - Linear system.?

Question

In the following case, the set of vectors {v1, · · · , vn} forms an orthonormal basis for the corresponding Euclidean vector space Rn.
Find an expression for the given vector w in terms of this basis.

n = 2
v1 = | (1/ √2) (1/ √2) |^T
v2 = | (1/ √2) (-1/ √2) |^T
w = | 4 9 |^T

Thanks for all the help, I'm really stuck on this one!

Answer 1

DC is right, and here is how you find the answer:

You need to find scalars a and b such that a(1/sqrt(2),1/sqrt(2)) + b(1/sqrt(2),-1/sqrt(2)) = (4,9). Therefore, (a/sqrt(2) + b/sqrt(2),a/sqrt(2) - b/sqrt(2)) = (4,9), and this gives you the system a/sqrt(2) + b/sqrt(2) = 4 and a/sqrt(2) - b/sqrt(2) = 9. Solve for a and b.

Answer 2

w = 13/sqrt2 v1 - 5/sqrt2 v2
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