Consider the following data \begin{tabular}{lr $\mathrm{x}$ & \multicolumn{1}{c}{$\mathrm{y}$} \ \hline \multicolumn{1}{1}{} &\ 0 & $-7.4406$ 1 & $9.5042$ 2 & $9.1978$ 3 & $25.5994$ 4 & $33.6258$ 5 & $11.2584$ 6 & $6.8671$ 7 & $25.1113$ 8 & $31.0453$ 9 & $40.3589$ 10 & $48.7861$ \end{tabular) Construct a least square fit of the data using polynomial basis functions (like $x^{i}, i=0,1,2, \cdots$ ) and trigonometric basis functions (like $\sin (ix), \cos (i x), i=1,2, \cdots) $. CS.JG. 17