91Ó°ÊÓ

Find the general solution of the system \(X^{\prime}=A X\) for the given \(m a-\) \(\operatorname{trix} A\). $$ A=\left(\begin{array}{rr} 4 & -13 \\ 2 & -6 \end{array}\right) $$

In Exercises 1 through \(5,\) replace the given equation by a system of first- order equations. \(y^{\prime \prime}+p y^{\prime}+q y=f(x)\).

Find the matrix requested given the following matrices: \(A=\left(\begin{array}{ll}1 & 2 \\ 3 & 1\end{array}\right) \quad B=\left(\begin{array}{rr}2 & 0 \\ 1 & -1\end{array}\right) \quad C=\left(\begin{array}{rr}1 & -1 \\ 1 & 2\end{array}\right)\) \(\quad A+2 B\).. \(A B+2 I\).

In Exercises 1 through \(7,\) find the general solution of the system \(X^{\prime}=A X\) for the given matrix A. In each case check on the linear independence of solutions by examining the Wronskian. $$ A=\left(\begin{array}{rr} 4 & 3 \\ -4 & -4 \end{array}\right) $$

Find the general solution of the system \(X^{\prime}=A X\) for the given \(m a-\) \(\operatorname{trix} A\). $$ A=\left(\begin{array}{rr} 3 & 5 \\ -1 & -1 \end{array}\right) $$

Solve the system \(X^{\prime}=A X\). $$A=\left(\begin{array}{ll}1 & -2 \\ 2 & -3\end{array}\right)$$

In Exercises 1 through \(5,\) replace the given equation by a system of first- order equations. \(y^{\prime \prime \prime}+p y^{\prime \prime}+q y^{\prime}+r y=f(x)\).

In Exercises 1 through \(7,\) find the general solution of the system \(X^{\prime}=A X\) for the given matrix A. In each case check on the linear independence of solutions by examining the Wronskian. $$ A=\left(\begin{array}{rrr} 1 & 2 & -1 \\ 0 & -1 & 3 \\ 0 & 0 & 2 \end{array}\right) $$

Find the matrix requested given the following matrices: \(A=\left(\begin{array}{ll}1 & 2 \\ 3 & 1\end{array}\right) \quad B=\left(\begin{array}{rr}2 & 0 \\ 1 & -1\end{array}\right) \quad C=\left(\begin{array}{rr}1 & -1 \\ 1 & 2\end{array}\right)\) \(\quad A+2 B\). \(\quad A C+B I\).

Find the general solution of the system \(X^{\prime}=A X\) for the given \(m a-\) \(\operatorname{trix} A\). $$ A=\left(\begin{array}{rr} 12 & -17 \\ 4 & -4 \end{array}\right) $$