I put the vectors in a matrix and reduced it, solved the determinant and got 0. This tells me that the vectors are linearly dependent. I am not sure how to figure out the non-trivial relation. This is my reduced matrix.
$$
\begin{pmatrix}
1& 0&-1/4 \\
0& 1& 1\\
0& 0& 0
\end{pmatrix}
$$
$$
A = \left\{\begin{matrix}
-60\\
-4\\
-72
\end{matrix}\right.
:
B = \left\{\begin{matrix}
-5\\
-1\\
-5
\end{matrix}\right.
:
C = \left\{\begin{matrix}
10\\
0\\
13
\end{matrix}\right.
$$
__A +__B +___C = 0
Find coefficients.
Best Answer
Found the RREF, set the free variable to 1, since it's linearly dependent and solved the system of equations to get coefficients.