Explanation

• For a vector field to be solenoidal, its divergence must be zero. The divergence of a vector field A = (x + 3y)i + (y - 2z)j + (x + mz)k is given by ∇ ⋅ A = ∂(x + 3y)/∂x + ∂(y - 2z)/∂y + ∂(x + mz)/∂z.
• Calculating the divergence:
  
• ∇ ⋅ A = 1 + 1 + m
• For the field to be solenoidal (∇ ⋅ A = 0), m must be -2.