Problems "GSL-matrix"

sudo apt install autoconf automake libtool
cd ~/local
git clone https://git.savannah.gnu.org/git/gsl.git
cd gsl
sh autoconf.sh  # and install what is missing
sh configure    # and install what is missing
make --jobs=3
make --jobs=3 check
sudo make install # installs in /usr/local by default
# you might want to add /usr/local/lib to your /etc/ld.so.conf

1. (Mandatory) Consider the following system of linear equations in the matrix form,

   
   
   [
    6.13 
    -2.90 
    5.86 
   ]
    [x0] 
    
    [6.23]
   
   
   [
    8.08 
    -6.31 
    -3.89 
   ]
    [x1] 
    = 
    [5.37]
   
   
   [
    -4.36 
    1.00 
    0.19 
   ]
    [x2] 
    
    [2.29]
   
   

   1. Solve it using GSL's [Householder solver for linear systems].

   2. Check that you have the correct solution by multiplying the original matrix (you need to save a copy of it as the routine destroys the matrix it is given) and the solution and comparing with the right-hand-side.

2. (Optional) Compute the eigenvalues and eigenvectors of 4-th order Hilbert matrix, H_ij = 1/(i + j + 1).