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2 answers:
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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
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.