(Solved): Three vectors v1,v2, and v3 are given. If they are linearly independent, show this; otherw ...

Three vectors $v_1,v_2$, and $v_3$ are given. If they are linearly independent, show this; otherwise, find a nontrivial linear combination of them that is equal to the zero vector. ${\mathbf{v}}_1=\left[\begin{array}{r}3\\ -7\\ -3\\ 7\end{array}\right],{\mathbf{v}}_2=\left[\begin{array}{r}-12\\ -6\\ -2\\ 5\end{array}\right],{\mathbf{v}}_3=\left[\begin{array}{r}4\\ 3\\ 1\\ -2\end{array}\right]$ Select the correct answer below, and fill in the answer box(es) to complete your choice. A. The vectors are linearly independent. The augmented matrix $\left[\begin{array}{llll}{\mathbf{v}}_1& {\mathbf{v}}_2& {\mathbf{v}}_3& 0\end{array}\right]$ has an echelon form $E=$ which has only the trivial solution. (Type an integer or simplified fraction for each matrix element.) B. The vectors are linearly dependent, because $4{\mathbf{v}}_1+||{\mathbf{v}}_2+\mid {\mathbf{v}}_3=0$. (Type integers or fractions.)