1. ## basis and dimension

Bit stuck step by step much appreciated

decide if each is a basis for r^3

(1) , (3)
(2) , (2)
(3) , (1)

and

(0), (1), (0)
(2), (1), (0)
(-1), (1), (0)

help much appreciated

Bit stuck step by step much appreciated

decide if each is a basis for r^3

(1) , (3)
(2) , (2)
(3) , (1)

and

(0), (1), (0)
(2), (1), (0)
(-1), (1), (0)

help much appreciated
The first one cannot be a basis for it has 2 elements. A basis for $\mathbb{R}^3$ will need 3 elements.

And the second one cannot be a basis for it contains the zero vector.