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.