Question

a set of vectors,A=[a+b,a,0,c,b+c], a,b,c belongs to R. how to find a basis and orthonormal basis for A? and how to prove it is a vector space....thank you

Answer 1

Use Gram-Schmidt on the set of vectors to find an orthonormal basis. To show it's a vector space, there are 8 or 9 definitions the space must satisfy. Google this.