91Ó°ÊÓ

Find the value of the determinant.

$\left|\begin{array}{ccc}4& −1& 2\\ 6& −1& 0\\ 1& −3& 4\end{array}\right|$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+y^2=4; \\ {x}^2+2x+y^2=0 \end{gathered}$$

Write the partial fraction decomposition of each rational expression:

$\frac{4}{x(x-1)}$.

Graph the inequality by hand.

$xâ‰\yen 4$

solve each system of equations using matrices.

If the system has no solution, say that it is inconsistent.

$$\begin{gathered} 6x+3y=12 \\ 2x-y=-2 \end{gathered}$$

Verify that the values of the variables listed are solutions of the system of equations.

$$\begin{gathered} \left\{\begin{array}{c}\begin{array}{rcl}3x+3y+2z& =& 4\\ x-y-z& =& 0\end{array}\\ 2y-3z=-8\end{array}\right. \\ x=1,y=-1,z=2;\left(1,-1,2\right) \end{gathered}$$

Write the augmented matrix of the given system of equations.

$\left\{\begin{array}{l}2x+3y-4z=0\\ x-5z+2=0\\ x+2y-3z=-2\end{array}\right.$

Write the partial fraction decomposition of each rational expression:

$\frac{3x}{(x+2)(x-1)}$.

Solve each linear programming problem.

Maximize$z=5x+3y$subject to$\left\{\begin{array}{l}xâ‰\yen 0\\ yâ‰\yen 0\\ x+yâ‰\yen 2\\ x+y≤8\\ 2x+y≤10\end{array}\right.$

Graph each inequality by hand.

$y≤2$