Question

Consider the following subset: W =(x, y, z) ∈ R^3; z = 2x - y from...

Consider the following subset:
W =(x, y, z) ∈ R^3; z = 2x - y from R^3.
 
Of the following statements, only one is true. Which?

(1) W is not a subspace of R^3

(2) W is a subspace of R^3
and {(1, 0, 2), (0, 1, −1)} is a base of W

(3) W is a subspace of R^3
and {(1, 0, 2), (1, 1, −3)} is a base of W

(4) W is a subspace of R^3
and {(1, 0, 2), (0, 1, −1), (−1, −1, −1)} is a
base of W

(5) W is a line in R^3 having (2, −1, −1) as a directing vector

(6) W is not a plane in R^3 having vector (2, −1, 1) as vector
normal
Math   Calculus   
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Answer #1

That means option 3 is correct.

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