1. If $p:(a, b) \rightarrow R$, $q:(a, b) \rightarrow R$, and $g:(a, b) \rightarrow R$ are continuous and $a < t_0 < b$, then there exists a unique function $y = \phi(t)$,   $\phi:(a, b) \rightarrow R$ that satisfies the initial value problem $y'' + p(t) y' + q(t)y = g(t)$,   $y(t_0) = y_0$,    $y'(t_0) = y_1$.

               A) True                        

2. If $A$ is a matrix whose elements consist of continuous functions of $t$, then there exists a unique function ${\bf x}(t) = {\bf f}(t)$ that satisfies the initial value problem ${\bf x}' = A{\bf x}$ ,   ${\bf x}(t_0) = {\bf x_0}$,    ${\bf x}'(t_0) = {\bf x_1}$.

                                        B) False

3. If $A$ is a matrix whose elements consist of continuous functions of $t$, then there exists a unique function ${\bf x}(t) = {\bf f}(t)$ that satisfies the initial value problem ${\bf x}' = A{\bf x}$ ,   ${\bf x}(t_0) = {\bf x_0}$.

               A) True                        

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