91Ó°ÊÓ

Find the cofactor of each element in the second row for each determinant. $$\left|\begin{array}{rrr} -2 & 0 & 1 \\ 1 & 2 & 0 \\ 4 & 2 & 1 \end{array}\right|$$

Find the value of each determinant. $$\left|\begin{array}{rrr} 1 & 2 & 0 \\ -1 & 2 & -1 \\ 0 & 1 & 4 \end{array}\right|$$

Find the value of each determinant. $$\left|\begin{array}{rrr} 1 & -2 & 3 \\ 0 & 0 & 0 \\ 1 & 10 & -12 \end{array}\right|$$

Solve each system by elimination. First clear denominators. $$\begin{aligned} &2 x-3 y=-7\\\ &5 x+4 y=17 \end{aligned}$$

Solve each system by elimination. First clear denominators. $$\begin{aligned} &5 x+4 y+2=0\\\ &4 x-5 y-23=0 \end{aligned}$$

Solve each system by using the inverse of the coefficient matrix. $$\begin{aligned} &x+3 y=-12\\\ &2 x-y=11 \end{aligned}$$

To meet a sales quota, a car salesperson must sell 24 new cars, consisting of small, medium, and large cars. She must sell 3 more small cars than medium cars, and the same number of medium cars as large cars. How many of each size must she sell?

Use the shading capabilities of your graphing calculator to graph each inequality or system of inequalities. $$y \leq x^{2}+5$$

Solve each system. $$\begin{aligned} &\frac{2}{x}+\frac{1}{y}=11\\\ &\frac{3}{x}-\frac{5}{y}=10 \end{aligned}$$

Solve each problem. Yogurt sells three types of yogurt: nonfat, regular, and super creamy, at three locations. Location I sells 50 gal of nonfat, 100 gal of regular, and 30 gal of super creamy each day. Location II sells 10 gal of nonfat, and Location III sells 60 gal of nonfat each day. Daily sales of regular yogurt are 90 gal at Location II and 120 gal at Location III. At Location II, 50 gal of super creamy are sold each day, and 40 gal of super creamy are sold each day at Location III. (a) Write a \(3 \times 3\) matrix that shows the sales figures for the three locations, with the rows representing the three locations. (b) The incomes per gallon for nonfat, regular, and super creamy are \(\$ 12, \$ 10,\) and \(\$ 15,\) respectively. Write a \(1 \times 3\) or \(3 \times 1\) matrix displaying the incomes. (c) Find a matrix product that gives the daily income at each of the three locations. (d) What is Yagel's Yogurt's total daily income from the three locations?