Exam 9: Systems and Matrices

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Does a square matrix with a row of all zeros have an inverse?

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x+6y=-18 -7x+5y=32

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of intersection specified on the graph are solutions of the system by substituting directly into both equations. - +=25 2y+x=5

Solve the system using a graphing calculator capable of performing row operations. Give solutions with values correct to the nearest thousandth. - 0.6x+4.9y-z=7 x-18y+10z=-1 3x+y-4.9z=

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

Solve the problem. -Find the dimensions of a rectangular garden with perimeter $62 \mathrm { yd }$ and area $220 \mathrm { yd } ^ { 2 }$ .

Solve the system by elimination. - 7x+9y=19 -5x+5y=-25

Solve each problem. -Le Boulangerie, a bakery, sells four main items: sweet rolls, bread, cakes, and pies. The amount of each ingredient (in cups, except for eggs) required for these items is given by matrix

Solve the problem. -The sum of the squares of the digits of a positive two-digit number is 61 , and the tens digit is 1 more than the units digit. Find the number.

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 2 & 1 & 4 \\ - 4 & 3 & - 1 \\ 7 & 4 & 0 \end{array} \right] ; 2$ times row 1 added to row 2

Evaluate the determinant. - $\left| \begin{array} { r r r } - 2 & - 7 & 0 \\ 9 & - 7 & 0 \\ 8 & - 7 & 0 \end{array} \right|$

Evaluate the determinant. - $\left| \begin{array} { l l l l } 0 & 0 & 0 & 1 \\ 8 & 9 & 9 & 9 \\ 2 & 2 & 1 & 2 \\ 7 & 8 & 4 & 7 \end{array} \right|$

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } - 5 & - 4 \\7 & 4\end{array} \right] + \left[ \begin{array} { r r } - 9 & 3 \\1 & 2\end{array} \right] - \left[ \begin{array} { r r } 7 & - 2 \\- 2 & 8\end{array} \right]$

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - x+y-2z-8=0 3x+z+6=0 2x-y+3z+14=0

Solve the problem. -A bakery sells three types of cakes, each requiring the amount of ingredients shown. To fill its orders for these cakes, the bakery used 72 cups of flour, 48 cups of sugar, and 60 eggs. How many cakes of each type were made?

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & - 2 & 5 \\1 & - 1 & 2 \\2 & - 3 & 7\end{array} \right]$

Use a graphing calculator and the method of matrix inverses to solve the system. Give five decimal places, if necessary. - \pix+ey+z=2 ex+\piy+z=4 x+ey+\piz=6

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y= -4=11

Solve the linear programming problem. -A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $\$ 2400$ , and the average monthly salary of an aide is $\$ 1100$ The camp can accommodate up to 45 staff members and needs at least 30 to run properly. The camp must have at least 10 aides and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost?

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. -A is $4 \times 4$ ; B is $4 \times 4$ .