Linear Algebra

[kickup]

let U=Span{u,v,w} be the subspace spanned by u, v, w where

...(0).....(4)......(2)
u=(3), v=(8), w=(7)
...(1).....(2).....(2)

find a subset of B so that B is a base for U

 

[DrSteve]

Put these vectors into a matrix and row reduce. You will see that w can be written as a linear combination of u and v.

More specifically, w = u + (1/2)v

This means that Span{u,v,w} = Span{u,v}, and thus B = {u,v} is a basis for U.