(3 points) Assume u4 is not a linear combination of {ui, u2, u3) Select the best

Question

(3 points) Assume u4 is not a linear combination of {ui, u2, u3) Select the best statement. A. {ui, u2, u3, u4} is a linearly independent set of vectors unless one or(???2, u3} is the zero vector. B. {ui , u2, u3, u4} could be a linearly independent or linearly dependent set of vectors depending on the vectors chosen C. u, u2, u3, u4^ is always a linearly independent set of vectors. D. u, u2, u3, u4^ is never a linearly independent set of vectors. E. u, u2, u3, u4} could be a linearly independent or linearly dependent set of vectors depending on the vector space chosen. F. none of the above

Explanation / Answer

Option A will be the best statement

Reason:

If we cannot write u4 as a linear combination of vectors u1,u2,u3 then set is linearly independent set

Also if all the vectos are nonzero then set is independent set.

Here,we cannot write u4 as a linear combination of u1,u2,u3,

So,set must be linearly independent unless one of u1,u2,u3 is zero vector.

Therefore option A is correct

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