Should I take Elementary Linear Algebra or Calculus III?

If your Calc III is multivariate/multivariable/vector calculus, that would generally be considered the hardest general math class you'll ever take.  It's all the calculus you've done but multi-dimensional and parametric, in multiple coordinate systems, and then some.  Linear algebra is setting up systems of equations in a linear form, that is, all equations form lines, which mean only simple coefficients with no exponents, so that you can solve the system with defined generalized matrix operations.

My add-on question is: would there be a benefit of waiting to take linear algebra after Calc IV (differential equations)