Consider this simple matrix number multiplication:

 lth = 200;
 mtx = RandomReal[{0, 1}, {lth, lth}];
 ls = RandomReal[{0, 1}, {lth}];
 
 Et = Function[{t}, Sin[(π t)/20] Sin[2 t]];
 Etc = Compile[{{t, _Real}}, Et[t], 
 CompilationOptions -> {"InlineCompiledFunctions" -> True, 
 "InlineExternalDefinitions" -> True}];


 Table[Etc[t]*mtx;, {t, 0., 20, 0.01}]; // AbsoluteTiming
 (* {0.244659, Null} *)

It seems that this is very slow, compared to matrix vector multiplication:
 
 Table[mtx.ls;, {t, 0., 20, 0.01}]; // AbsoluteTiming
 (* {0.038151, Null} *)

Moreover, the matrix addition also seems to be slow

 Table[mtx + mtx;, {t, 0., 20, 0.01}]; // AbsoluteTiming
 (* {0.153648, Null} *)

**Question:** So why the matrix number multiplication and addition so much slower than the matrix vector multiplication? Are there ways to speed them up?

I'm using 10.3 on OS X 10.11.4.

---
**Edit**

The slowness of the matrix number multiplication doesn't seem to come from `Etc`, for example:

 Table[Etc[t];, {t, 0., 20, 0.01}]; // AbsoluteTiming
 (* {0.001614, Null} *)
 
 Table[1.*mtx;, {t, 0., 20, 0.01}]; // AbsoluteTiming
 (* {0.235871, Null} *)

---
**Edit 2**

Here is a comparison to Matlab:

 lth=200;
 mtx=rand(lth);
 ls=rand(lth,1);
 
 
 tic;
 for t=0:0.01:20
 mtx2=1.*mtx;
 end
 toc
 
 
 tic;
 for t=0:0.01:20
 mtx2=mtx*ls;
 end
 toc
 
 

> Elapsed time is 0.034530 seconds.
> Elapsed time is 0.015745 seconds.

Mathematica is as fast as Matlab in matrix vector multiplication, but about 7X slower in the matrix number multiplication.