Check linear Independence of vectors with a non-square matrix

Question

In a ℝ¹⁵ space, I take two vector that I would like to check if they are linear independent. They are:

-0.0049    0.0000
-0.0085    0.0000
 0.3555    0.0000
 0.4364    0.3921
 0.4267   -0.2660
-0.3448    0.1596
-0.3215   -0.3921
-0.3694    0.2660
-0.2737    0.1596
-0.0992   -0.2660
 0.0758   -0.3921
 0.1163   -0.1596
 0.0348    0.2660
-0.1246    0.3921
 0.1467   -0.1596

How do I do it? These are two vectors for the x,y and z of 5 particles.

Thanks in advance for the help.

Answer 1

Hint:

Two vectors are linearly independent if none of them is a linear combination of the other.

Answer 2

These two vectors are linearly independent. The first coordinate is $0$ for the right vector but non-zero for the left vector whereas the forth is non-zero for both.

In general, if $v_1$ is the first vector and $v_2$ is the second vector, they are linearly dependent if you can find a real number $\alpha\neq 0$ such that $$v_1=\alpha v_2$$