91Ó°ÊÓ

Find the partial fraction decomposition. \(\frac{x+34}{x^{2}-4 x-12}\)

Sketch the region \(R\) determined by the given constraints, and label its vertices. Find the maximum value of \(C\) on \(R\) $$\begin{array}{lll} C=3 x+y ; & x \geq 0, y \geq 0 \\ 3 x-4 y \geq-12, & 3 x+2 y \leq 24, & 3 x-y \leq 15 \end{array}$$

Use matrices to solve the system. $$\left\\{\begin{array}{rr} 5 x+2 y-z= & -7 \\ x-2 y+2 z= & 0 \\ 3 y+z= & 17 \end{array}\right.$$

Exer. \(3-12:\) Find the inverse of the matrix if it exists. $$\left[\begin{array}{rr} 2 & -4 \\ 1 & 3 \end{array}\right]$$

Sketch the graph of the Inequality. $$2 x+3 y \geq 2 y+1$$

Find, if possible, \(A+B, A-B, 2 A,\) and \(-3 B\). $$A=\left[\begin{array}{rr} 6 & -1 \\ 2 & 0 \\ -3 & 4 \end{array}\right], \quad B=\left[\begin{array}{rr} 3 & 1 \\ -1 & 5 \\ 6 & 0 \end{array}\right]$$

Find all the minors and cofactors of the elements in the matrix. $$\left[\begin{array}{rrr} 2 & 4 & -1 \\ 0 & 3 & 2 \\ -5 & 7 & 0 \end{array}\right]$$

Use the method of substitution to solve the system. $$\left\\{\begin{aligned} y^{2} &=1-x \\ x+2 y &=1 \end{aligned}\right.$$

Use matrices to solve the system. $$\left\\{\begin{aligned} 4 x-y+3 z &=6 \\ -8 x+3 y-5 z &=-6 \\ 5 x-4 y &=-9 \end{aligned}\right.$$

Find all the minors and cofactors of the elements in the matrix. $$\left[\begin{array}{rrr} 5 & -2 & 1 \\ 4 & 7 & 0 \\ -3 & 4 & -1 \end{array}\right]$$