Chapter 10, Problem 23P

Let the function be defined on the interval $\left[0,2\right]$ as follows:

$f\left(x\right)=\left\{\begin{array}{cc}ax+b,& 0\le x\le 1\\ cx+d,& 1\le x\le 2\end{array}\right\}$

Determine the constants a, b, c, and d so that the function f satisfies the following:

• $f\left(0\right)=f\left(2\right)=1$.

•f is continuous on the entire interval.

• $a+b=4$.

Derive and solve a system of linear algebraic equations with a matrix form identical to Eq. (10.1).