Consider the following system of linear equations
\[\left[ {\begin{array}{*{20}{c}} 2&1&{ - 4} \\ 4&3&{ - 12} \\ 1&2&{ - 8} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\text{x}} \\ {\text{y}} \\ {\text{z}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} \alpha \\ 5 \\ 7 \end{array}} \right]\]
Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of \[\alpha \], does this system of equations have infinitely many solutions?

A. 0

B. 1

C. 2

D. infinitely many

Answer: Option B