I test the following command in Octave, Scilab and Matlab prompt.
>> A = rand(10000,10000);
>> B = rand(10000,1);
>> tic,A\B;, toc
The timings were around, respectively, 40, 15.8 and 15.7 sec. For comparison Mathematica's performance was
In[7]:= A = RandomReal[{0, 1}, {10000, 10000}];
In[9]:= B = RandomReal[{0, 1}, 10000];
In[10]:= Timing[LinearSolve[A, B];]
Out[10]= {14.125, Null}
Does this indicate that Octave is not so capable as the rest of the softwares in the field of linear equations?
I think that your tests are flawed. The algorithms behind A\B make use of the special patterns and structures in the systems of equations, so execution time depends very much on what random(10000,10000) has generated. On three different runs with Octave 4.0.0 on my machine, your code returns 7.1s, 95.1s and 16.4s. That indicates that the first matrix generated by random was probably sparse, and that could have been the case when you tested your code with Scilab and Matlab. So unless you make sure that the algorithms are evaluating the same thing, or unless you average the execution time in a sound manner (that is not very trivial to find for me), then it doesn't make sense to compare them as you did.