# How to find 3 linearly independent vector pairs but together they are linearly dependent?

Given 3 vectors $v_1, v_2, v_3 \in \mathbb{R^3}$ find an example such that {$v_1, v_2$}, {$v_1, v_3$}, {$v_2, v_3$} are linearly independent but {$v_1, v_2, v_3$} is linearly dependent.

The problem seems to be very simple yet I can't come up with a solution.

• "Given 3 vectors"? If the 3 vectors are given to you, what is there to "find" for you? – Henning Makholm Apr 8 '17 at 14:57
• Any 3 vectors in a 2D subspace of $R^3$ but where no two of them are parallell. You can for example make this sure by choosing one vector, and rotating twice along the same axis orthogonal to first vector some angle which is not any integer multiple of a fourth revolution. – mathreadler Apr 8 '17 at 15:17

$$v_1=(1,0,0), v_2=(1,1,0), v_3=(0,1,0)$$
For example, you can choose any two non-collinear vectors $v_1$, $v_2$, and take $$v_3 = v_1+v_2.$$