For which values of a b c is a b c element of span1 2 1 1 1

For which values of a, b, c is (a, b, c) element of span{(1, 2, -1), (1, -1, 2), (1, 0, 1)}?

Solution

a can be in the range of x co-ordinates of the 3 vector points
Hence a can be from 1 to 1 to 1 which is a=1

b can be in the range of y co-ordinates of the 3 vector points
hence b can be from 2 to -1 to 0 or b= [-1,2] (in that range)
c can be in the range of z co-ordinates of the 3 vector points
hence c can be from -1 to 2 to 1 or c= [ -1,2]

hence a = {1}
b= [-1,2]
c= [ -1,2]