Answer:
Step-by-step explanation:
A vector in R^3 which is not in the span of the set S {(1,2,-2) and (2,-1,1)
If a vector is in the span it can be represented as a linear combination of these two vectors
Let S1 = (1,2,-2) and S2 = (2,-1,1)
i.e. any vector which is of the form
![\alpha S1+\beta S2\\=(\alpha +2\beta,2\alpha -\beta,-2\alpha +\beta)](https://tex.z-dn.net/?f=%5Calpha%20S1%2B%5Cbeta%20S2%5C%5C%3D%28%5Calpha%20%2B2%5Cbeta%2C2%5Calpha%20-%5Cbeta%2C-2%5Calpha%20%2B%5Cbeta%29)
Where alpha and beta are any real numbers
Any vector not in this form will not be in the span
i.e. say if alpha = beta =1,
then spanned vector = (3,1,-1)
If we change one coordinate alone say
(3,0,-1) this cannot be represented as a linear combination hence this would be the answer.