[Math] converting orthogonal set to orthonormal set

matricesorthonormalvectors

Verify that the set of vectors:

  {(5,0), (0,5)}

is orthogonal with respect to the inner product:

 < u, v > = 4u1v1 + u2v2 on R2 ;

then convert it to an orthonormal set by normalizing the vectors.

I thought this would be simple, but it has proven to be more complicated than i thought. I must not understand part of the process. I verified that the set was orthogonal by 

0 = 4(5*0) + (0*5)

now to make theses vectors orthonormal I followed this formula:

||V|| = < V, V >^1/2 = ( 4V1V1 + V2V2 )^1/2

and my results were as follows:

{(1/2,0), (0,1)}

But no matter how I give it to the computer it wont take it. Is this incorrect?

Best Answer

I do not know what your computer has done, But I know that you are right.

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