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negation

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## Homework Statement

a)Which of these subsets contain the zero vector 0 = (0, 0, 0, 0) ?

b)Which of these subsets are subspaces of R4 ?S = { (x1, x2, x3, x4) | x4 = -6 - 5 x1 }

T = { (x1, x2, x3, x4) | x4 is an integer }

U = { (x1, x2, x3, x4) | x1 + x4 ≤ -6 }

## The Attempt at a Solution

If a set is closed under addition and closed under scalar multiplication, then it contains the zero vector. But isn't the definition of subset such that a vector space is a linear combination of all other vector. I'm terribly lost!

I'm really struggling badly with this. Can someone give me a leg up?

S = (x1,x2,x3,x4) and let W = (w1,w2,w3,w4)

then S+W= (x1+w1,x2+w2,x3+w3,x4+w4)

(x4+w4) = -6-5(x1+w1) (closed under addition?) (Where do I go from here?)

Let k = scalar

KW = (Kw1, kw2,kw3,kw4)

kw4 = -6-5(kw1) (closed under scalar?)

There are values for me to determine if the left hand side values equals the right hand side values.

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