Given the matrices A, B and C as follows
A = \begin{bmatrix} 1 & 5 & 1 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{bmatrix}, B = \begin{bmatrix} -1 & 1 & 1 \\ 4 & 1 & -2 \\ 0 & -2 & 0 \end{bmatrix}, and C = \begin{bmatrix} 5 & 13 & 1 \\ -5 & -2 & 7 \\ 0 & 7 & 3 \end{bmatrix}.
(1) What is the vector space in which belong the matrices A, B, C?
(2) Show that C is a linear combination of A and B by finding the coefficients of the linear combination.
(3) Are A, B, C dependents or independents vectors in their corresponding vector space? Explain why?