let p(t) be the natueal cubic spline which interpolates the data
(0,5), (1, 9), (2, 2), (3, -29), (4, 65), (5, -110)
with coefficient matrix
[ -3 0 a3 -1 2 ]
[ 0 -9 b3 -3 -6 ]
[ 7 -2 c3 -32 -41]
[ 5 9 -2 -29 -65]
such that each cubic in the spline is of the form
Pₖ (t) = aₖ(t-tₖ₋₁)³ + bₖ (t-tₖ₋₁)²+ck (t-tₖ₋₁)+dₖ, t∈ [tₖ₋₁,tk]
Determine the coefficient a₃.