Chapter 6.1, Problem 3P

For problem 1-8, verify directly from Definition 6.1.3 that the given mapping is a linear transformation.

$T:C^2\left(I\right)\to C^0\left(I\right)$ defined by $T\left(y\right)=\left(y^{″}+a_1{y}^{\prime }+a_{2}y\right)$,

where $a_1$ and $a_2$ are the functions defined on $I$.