Let p(t) be the natural 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.