91Ó°ÊÓ

Write each system of equations in the form \(\left\\{\begin{array}{l}A x+B y=E \\\ C x+D y=F\end{array}\right.\) and then solve the system. $$\left\\{\begin{aligned} 3(x+y) &=1 \\ -2 x &=-y+2 \end{aligned}\right.$$

Write the partial fraction decomposition of each rational expression. $$\frac{4 x+1}{(x+2)\left(x^{2}+3\right)}$$

Use matrix inversion to solve the system of equations. $$\left\\{\begin{aligned}3 x+7 y &=-11 \\\x+2 y &=-3\end{aligned}\right.$$

Solving Systems of Equations Using Matrices. $$\left\\{\begin{aligned}5 x+3 y &=-1 \\\\-10 x-6 y &=2\end{aligned}\right.$$

Solving Systems of Equations Using Matrices. $$\left\\{\begin{array}{rr}2 x+4 y= & 5 \\\\-4 x-8 y= & -10\end{array}\right.$$

Write each system of equations in the form \(\left\\{\begin{array}{l}A x+B y=E \\\ C x+D y=F\end{array}\right.\) and then solve the system. $$\left\\{\begin{aligned} 2 x &=-3 y+4 \\ \frac{x+y}{3} &=1 \end{aligned}\right.$$

Write the partial fraction decomposition of each rational expression. $$\frac{x^{2}+3}{(x-1)\left(x^{2}+1\right)}$$

For the given matrices \(A\) and \(B\), evaluate (if defined) the expressions ( \(a\) ) \(A B,\) ( \(b\) ) \(3 B-2 A\), and (c) \(B A\). For any expression that is not defined, state the reason. $$A=\left[\begin{array}{ll}9 & -4 \\\7 & -3\end{array}\right] ; \quad B=\left[\begin{array}{rr}4 & 0 \\\\-7 & 5\end{array}\right]$$

Use Cramer's Rule to solve the system of equations. $$\left\\{\begin{array}{r} x-y=-3 \\ 4 x+y=0 \end{array}\right.$$

Use matrix inversion to solve the system of equations. $$\left\\{\begin{aligned}4 x-3 y &=1 \\\2 x-y &=-1\end{aligned}\right.$$