Science:Math Exam Resources/Courses/MATH307/December 2012/Question 01 (e)/Hint 1

In part (d) we found that, in order for p(x) to have zero slope at x = 0 and x = 2 and pass through the given points, the coefficients $\mathbf {a} =s_{1}\mathbf {a} _{1}+s_{2}\mathbf {a} _{2}$ would need to satisfy

${\begin{bmatrix}-4&1\\-2&1\\0&1\end{bmatrix}}{\begin{bmatrix}s_{1}\\s_{2}\end{bmatrix}}={\begin{bmatrix}2\\2\\1\end{bmatrix}}$

How can we find the least square solution of the system Cs = c above?