(Solved): Determine if the columns of the matrix form a linearly independent set. \[ \left[\begin{array}{rrrr ...

Determine if the columns of the matrix form a linearly independent set. \[ \left[\begin{array}{rrrr} 1 & 2 & -3 & 8 \\ 2 & 5 & -4 & 8 \\ 3 & 8 & -2 & -4 \end{array}\right] \] Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. The columns of the matrix do not form a linearly independent set because there are more entries in vector, than there are vectors in the set, (Type whole numbers.) B. The columns of the matrix do not form a linearly independent set because the set contains more vect than there are entries in each vector, (Type whole numbers.) C. Let A be the given matrix. Then the columns of the matrix form a linearly independent set since the ve equation, \( A x=0 \), has only the trivial solution. D. The columns of the matrix form a linearly independent set because at least one vector in the set is a constant multiple of another.