$$

please use GNU octave

Question $2$: $20$ Marks

The Hilbert matrix is a square $nn$ matrix defined by

$H_{ij}^{(n)}=\frac{1}{i+j-1}$

Define $b^{(n)}$ to be a column vector of dimension $n,$ and with each element $1.$ Construct $b^{(n)}$ and $H_{ij}^{(n)},$ and then solve for $x^{(n)},$ given that $H_{ij}^{(n)}{x}^{(n)}=b^{(n)},$ in the cases $n=4,7,10$ and $13.$ Comment on the results.