- #1

negation

- 818

- 0

## Homework Statement

U= { (x

_{1}, x

_{2}, x

_{3}, x

_{4}) | x1 x3 ≥ -5 }

## The Attempt at a Solution

Let x = (1,2,3,4) and y = (1,2,3,4)

x+ y = (2,4,6,8)

x

_{1}x

_{3}= 2x6 = 12

12 >-5 so closure by addition is fulfilled.

I've been hearing contradicting information-some state that any 1 test of the 3 is a sufficient condition.

Should I perform the closure by scalar multiplication, it can be easily shown that U is not a subspace of R

^{4}. Is there a less tedious way to determine that a vector is not an subspace?