91Ó°ÊÓ

Find the inverse of the matrix if it exists. $$\left[\begin{array}{rr} 0.4 & -1.2 \\ 0.3 & 0.6 \end{array}\right]$$

Graph each linear system, either by hand or using a graphing device. Use the graph to determine whether the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it. $$\left\\{\begin{aligned}x-y &=4 \\\2 x+y &=2\end{aligned}\right.$$

Find the partial fraction decomposition of the rational function. $$\frac{5}{(x-1)(x+4)}$$

Evaluate the minor and cofactor using the matrix \(A\) $$A=\left[\begin{array}{rrr} 1 & 0 & \frac{1}{2} \\ -3 & 5 & 2 \\ 0 & 0 & 4 \end{array}\right]$$ $$M_{12}, A_{12}$$

Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system. \(\left\\{\begin{aligned} 2 x-y+3 z &=2 \\ x+2 y-z &=4 \\\\-4 x+5 y+z &=10 \end{aligned}\right.\) Eliminate the \(x\) -term from the third equation.

Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system. \(\left\\{\begin{aligned} x-4 y+z &=3 \\ y-3 z &=10 \\ 3 y-8 z &=24 \end{aligned}\right.\) Eliminate the \(y\) -term from the third equation.

Evaluate the minor and cofactor using the matrix \(A\) $$A=\left[\begin{array}{rrr} 1 & 0 & \frac{1}{2} \\ -3 & 5 & 2 \\ 0 & 0 & 4 \end{array}\right]$$ $$M_{13}, A_{13}$$

Graph each linear system, either by hand or using a graphing device. Use the graph to determine whether the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it. $$\left\\{\begin{array}{l}2 x-y=4 \\\3 x+y=6\end{array}\right.$$

Find the inverse of the matrix if it exists. $$\left[\begin{array}{lll} 4 & 2 & 3 \\ 3 & 3 & 2 \\ 1 & 0 & 1 \end{array}\right]$$

Graph the inequality. $$x^{2}+(y-1)^{2} \leq 1$$