91Ó°ÊÓ

Find the inverse of the given matrix \(\mathbf{A}\) in each of Exercises 13-24. $$ \mathbf{A}=\left(\begin{array}{lll} 3 & 2 & 4 \\ 1 & 4 & 2 \\ 2 & 2 & 3 \end{array}\right) $$

Use the operator method described in this section to find the general solution of each of the linear systems in Exercises 1-26. $$ \begin{aligned} &2 x^{\prime}+y^{\prime}-x-y=1 \\ &x^{\prime}+y^{\prime}+2 x-y=t \end{aligned} $$

Find the general solution of each of the linear systems in Exercises 1-26. $$ \begin{aligned} &x^{\prime}=x-2 y \\ &y^{\prime}=2 x-3 y \end{aligned} $$

Use the operator method described in this section to find the general solution of each of the linear systems in Exercises 1-26. $$ \begin{aligned} &x^{\prime \prime}+y^{\prime}=e^{2 t} \\ &x^{\prime}+y^{\prime}-x-y=0 \end{aligned} $$

Find the inverse of the given matrix \(\mathbf{A}\) in each of Exercises 13-24. $$ \mathbf{A}=\left(\begin{array}{lll} 1 & 2 & 0 \\ 3 & 7 & 1 \\ 1 & 3 & 3 \end{array}\right) $$

Find the inverse of the given matrix \(\mathbf{A}\) in each of Exercises 13-24. $$ \mathbf{A}=\left(\begin{array}{rrr} 1 & 0 & -1 \\ 4 & 2 & 1 \\ 2 & 1 & 3 \end{array}\right) $$

Find the general solution of each of the linear systems in Exercises 1-26. $$ \begin{aligned} &x^{\prime}=3 x-y \\ &y^{\prime}=x+y \end{aligned} $$

Find the inverse of the given matrix \(\mathbf{A}\) in each of Exercises 13-24. $$ \mathbf{A}=\left(\begin{array}{rrr} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end{array}\right) $$

Find the general solution of each of the linear systems in Exercises 1-26. $$ \begin{aligned} &x^{\prime}=8 x-4 y \\ &y^{\prime}=x+4 y \end{aligned} $$

Use the operator method described in this section to find the general solution of each of the linear systems in Exercises 1-26. $$ \begin{aligned} &x^{\prime \prime}-y^{\prime}=e^{t} \\ &x^{\prime}+y^{\prime}-4 x-y=2 e^{t} \end{aligned} $$