Question

.show that the following are spanning sets for R3
{(1,1,1)transpose (1,1,0)transpose (1,0,0)transpose}

Answer 1

any coordinate in R3 (a,b,c) can be given in terms of linear combination of the three vectors...

Answer 2

but how to find linear combination

Answer 3

x + y + z = a
x + y = b
x = c
y = b - c
z = a - b

hence linear combination is (a - b)(1,1,1) + (b-c) (1,1,0) + c(1,0,0) for any (a,b,c)