Let W be the set of all vectors [x_1 x_2 x_3 x_4] such that x_1 - 2 x_2 = 4x_3 a
ID: 3110953 • Letter: L
Question
Let W be the set of all vectors [x_1 x_2 x_3 x_4] such that x_1 - 2 x_2 = 4x_3 and 2x_1 = x_3 + 3x_4. Determine if W is a vector space and check the correct answer(s) below. W is a vector space because it can be written as N(A) for some matrix A. W is a vector space because it is in R^4. W is not a vector space because it does not have additive closure. W is a vector space because it has a zero element. W is not a vector space because it is not closed w.r.t scalar multiplication. W is not a vector space because it does not have a zero element.Explanation / Answer
Yes W is a vector space since it a subspace of R4. So option C, E and F are false.
Option B and D are not enough for a set to become a vector subspace.
Therefore option A is correct.
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