Let

*v *

= [1

1

0]

and *w *=

[2

0

2]

both are elements of R cubed*.*

Consider the set

*E *of all column vectors *u *in Rcubedthat can be written as *u *= *av *+ *bw *for some *a, b ∈ *R:

*E *

= *{u ∈ *R3 *| u *= *av *+ *bw *for some *a, b ∈ *R*}.* (*E *is sometimes referred to as the plane spanned by *v *and *w*.)

Now, given a 1 *× *3 matrix *A *(that is, a row vector), and an element *u ∈ E *we can form *Au*

which is a 1

*× *1 matrix (and hence a real number). Find all row vectors *A *such that *Au *= 0 for all *u ∈ E*.

(*Remark: *In other words, find all 1 *× n *matrices *A *such that *E *is a subset of the set of

solutions of *AX *= 0.) I'm completely lost on this one, so any help would be great.