Given system of equations is in form AX=B.
For infinitely many solutions here, effectively we have only two variables i.e. w=(y-4z). but they should be consistent i.e. rank(A)=rank(AB)<3(no. of variables)
Since column2 and column3 are dependent so make column3 all zero. So we got rank(A)=2
Now for the augmented matrix, AB put all zero column at last because it's of no use it will give 0 determinant value of all 3*3 submatrices.
After excluding that dependent column, we got a 3*3 matrix, solving it gives alpha= .2 this is single value.
Or see the image below
Option B ...
Note: The row rank and the column rank of a matrix A are equal. Here column rank is easy to find for A. And then for AB we must get rank 2 for having infinite solutions.
P.S. -- Ignore that "3 equation and 2 variable" in the image.