The vector x is in H = Span {v_{1}, v_{2}} and find the beta-coordinate vector [x]_{beta}



Answered question


The vector x is in H=Span v1,v2
and find the beta-coordinate vector [x]β

Answer & Explanation



Skilled2021-01-26Added 75 answers

Let vector x is in a vector space V and β=b1,b2,,bn is a basis for V,
then the beta- coordinates of x are the weights c1,c2,...,cn or [x]β=β[c1c2cn] such that x=c1b1+c2b2++cnbn.
The vectors v1=[115107],v2[1481310],and x=[19131815]
Here β=v1,v2 and H=Spanv1,v2.
Therefore, for showing x is in H, show that the vector equation x=x1v1+x2v2 has a solution.
Write the given vectors as an augmented matrix [v1v2x] and find the row reduced form of the matrix.
On further simplification the matrix becomes,

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?