Linear Systems of DEs Show that the systems of linear differential equations given in Problems 1

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Accepted Answer

Step 1: Define the transformation and the space.
We are given a transformation ( T: mathcal{C}^1

Linear Systems of DEs Show that the systems of linear differential equations given in Problems 18 and 19 are linear transformations, where $x=x(t)$ and $y=y(t) \in \mathcal{C}^1(l)$. $T(x, y)=\left(x+y^{\prime}, y-2 x+y^{\prime}\right)$