Chapter 5.FR2, Problem 15E

To determine

(a)

To prove:

If $i\ne j$, then $P_i\left(x_j\right)=0$.

To determine

(b)

To prove:

The equation $P_i\left(x_i\right)=1$.

To determine

(c)

To prove:

The plane $y_1{P}_1+y_2{P}_2+y_3{P}_3$ passes through the points $\left(x_1,y_1\right)$, $\left(x_2,y_2\right)$, and $\left(x_3,y_3\right)$.

To determine

(d)

The quadratic determined by $\left(1,2\right)$, $\left(2,5\right)$, and $\left(3,6\right)$ using Lagrangian polynomials.