Exam 9: Systems and Matrices

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 6 & - 3 & 6 & - 4 \\6 & - 2 & - 4 & - 3 \\12 & - 5 & 2 & - 7 \\0 & - 6 & 12 & 0\end{array} \right]$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - y=-8x+16 x+y=4

Evaluate the determinant. - $\left| \begin{array} { r r r r } 3 & - 2 & 2 & - 1 \\4 & 1 & 1 & 6 \\- 3 & 2 & - 2 & 1 \\5 & 0 & 3 & - 2\end{array} \right|$

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

The solution set of the system $y _ { 1 } = 2 x + 3$ and $y _ { 2 } = - x + 9$ is $\{ ( 2,7 ) \}$ . Using slopes and $y$ -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Find the partial fraction decomposition for the rational expression. - $\frac { 12 x ^ { 2 } - 23 x + 20 } { ( x - 4 ) \left( x ^ { 2 } + 4 \right) }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Let $A = \left[ \begin{array} { r r } 1 & 4 \\ 3 & - 4 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 1 & 4 \\ - 5 & - 4 \end{array} \right]$ . Does the matrix A - B have an inverse?

Solve the system by elimination. - +=4 +=-3

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - +=13.85 x=3y-1

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 2x+8y=7 4x+16y=5

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - 2x+4y+8z=40 x+2y+4z=-10 x+y+z=-4

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function $= 3 x + y$ ; maximum

Solve the problem. -A television manufacturing company has two different factories. The profit function for Factory I when $x$ televisions are manufactured and sold is as follows: $P ( x ) = - 0.07 x ^ { 2 } + 25 x - 250$ The profit function for Factory II when $x$ televisions are manufactured and sold is as follows: $P ( x ) = - 0.075 x ^ { 2 } + 35 x - 1500$ For what number of televisions is the profit the same at both factories, and what is the profit?

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - xy=30 x+y=-11

The solution set of the system $y _ { 1 } = - x + 5$ and $y _ { 2 } = - 2 x + 7$ is $\{ ( 2,3 ) \}$ . Using slopes and $y$ -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Solve the system. - $\frac { 2 } { x } + \frac { 3 } { y } = \frac { 11 } { 15 }$ $\frac { 4 } { x } - \frac { 6 } { y } = \frac { 2 } { 15 }$

Find the dimension of the matrix. - $\left[ \begin{array} { c c c } 4 & 9 & - 3 \\1 & 8 & - 8\end{array} \right]$

Solve the equation for x. - $\left| \begin{array} { l l } x & 1 \\2 & x\end{array} \right| = - 1$

Provide an appropriate response. -Which one of the following is a description of the graph of the solution set for the system below? $4 x ^ { 2 } + 9 y ^ { 2 } < 36$ $y < - 2$

Solve the problem. -A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 5% cement should he mix with 14 bags of 14.5% cement to produce a mix containing 12% cement?