91Ó°ÊÓ

Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system. \(\left\\{\begin{array}{rr}-5 x+2 y-3 z= & 3 \\ 10 x-3 y+z= & -20 \\ -x+3 y+z= & 8\end{array}\right.\) Eliminate the \(x\)-term from the second equation.

Find the partial fraction decomposition of the rational function. $$\frac{2 x}{(x-1)(x+1)}$$

Perform the matrix operation, or if it is impossible, explain why. $$\left[\begin{array}{rr} 1 & 2 \\ -1 & 4 \end{array}\right]\left[\begin{array}{rrr} 1 & -2 & 3 \\ 2 & 2 & -1 \end{array}\right]$$

Graph the inequality. $$y>1$$

Find the determinant of the matrix, if it exists. $$\left[\begin{array}{rr} 2.2 & -1.4 \\ 0.5 & 1.0 \end{array}\right]$$

Finding the Inverse of a Matrix Find the inverse of the matrix if it exists. $$\left[\begin{array}{rr}-7 & 4 \\\8 & -5\end{array}\right]$$

Two equations and their graphs are given. Find the intersection point(s) of the graphs by solving the system. (Graph cannot copy) $$\left\\{\begin{aligned} x+y &=2 \\ 2 x+y &=5 \end{aligned}\right.$$

Perform the matrix operation, or if it is impossible, explain why. $$\left[\begin{array}{rr} 2 & -3 \\ 0 & 1 \\ 1 & 2 \end{array}\right]\left[\begin{array}{l} 5 \\ 1 \end{array}\right]$$

Finding the Inverse of a Matrix Find the inverse of the matrix if it exists. $$\left[\begin{array}{rr}6 & -3 \\\\-8 & 4\end{array}\right]$$

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