The "coordinate vectors" of any vector u is the ordered triple (a, b, c) where a(1,0,1)+ b(1,1,0)+ c(0,1,1)= v.

So you need (a,b,c) such that a(1,0,1)+ b(1,1,0)= c(0,1,1)= (1, 0, 0).

That is the same as saying (a, 0, a)+ (b, b, 0)+ (0, c, c)= (a+b, b+ c, a+ c)= (1, 0, 0) or a+b= 1, b+ c= 0, a+ c= 0. Solve those equations for a, b, and c.

"T" has nothing to do with this question!