I need to find a basis for the following:
{x belongs to R5, x1=x2, x3=x4) in R5
Let,
x1=x2=s
x3=x4=t
x5=r
Any element in this subspace is,
[x1 x2 x3 x4 x5] = [s s t t xr]
Write as,
[s s 0 0 0] + [0 0 t t 0] + [0 0 0 0 r]
Factor,
s[1 1 0 0 0] + t[0 0 1 1 0] + r[0 0 0 0 1]
We can see that,
{[1 1 0 0 0], [0 0 1 1 0], [0 0 0 0 1]}
Is the basis for this subspace.