Exam 9: Systems and Matrices

Provide an appropriate response. -Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $\left[ \begin{array} { r r r | r } 1 & - 15 & 7 & 19 \\0 & 1 & 14 & - 8 \\0 & - 9 & 20 & - 2\end{array} \right]$ What row transformation would you perform next?

Graph the inequality. - $y \leq 3 x-x^{2}$

Solve the problem. -Given $A = \left[ \begin{array} { r r } 3 & - 2 \\ - 4 & 4 \end{array} \right]$ , find $A ^ { 2 }$ .

Solve the system using a graphing calculator capable of performing row operations. Give solutions with values correct to the nearest thousandth. - x-0.9y+z=-8 x-y+2z= 6.2x+16y-5z=

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 8x-10y=1 -16x+20y=1

Evaluate the determinant. - $\left| \begin{array} { l l l l } 7 & 8 & 6 & 2 \\7 & 1 & 1 & 8 \\6 & 3 & 8 & 2 \\3 & 1 & 7 & 5\end{array} \right|$

Solve each problem. -Mikeʹs Bait Shop sells three types of lures: discount, normal, and professional. Location I sells 37 discount lures, 100 regular lures, and 30 professional lures each day. Location II sells 20 discount Lures and Location III sells 60 discount lures each day. Daily sales of regular lures are 90 at Location II and 120 at Location III. At Location II, 15 expert lures are sold each day, and 40 expert Lures are sold each day at Location III. Write a 3 × 3 matrix that shows the sales figures for the three locations, with the rows representing The three locations. The incomes per lure for discount, normal, and professional lures are $3, $8, And $17, respectively. Write a 3 × 1 matrix displaying the incomes. Find a matrix product that gives The daily income at each of the three locations.

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 $1 \times 4$ ; B is $1 \times 4$ .

Solve the system. - +=- -=-

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function $= 2 x + 4 y ;$ maximum

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l } \mathrm { a } \\ 5 \\ 3 \end{array} \right] = \left[ \begin{array} { l } 3 \\ \mathrm { x } \\ 3 \end{array} \right]$

Provide an appropriate response. -Fill in the blank to complete the statement. Two matrices are equal if they have the same ? and if all corresponding elements are equal.

Graph the solution set of the system of inequalities. -

Find the value of the determinant. - $\left| \begin{array} { l l } 0 & - 3 \\- 9 & 0\end{array} \right|$

Evaluate the determinant. - $\left| \begin{array} { r r r } 7 & - 3 & 9 \\ 0 & 5 & 1 \\ 0 & 0 & - 5 \end{array} \right|$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - 7+8 =4 -2+7 =49

Solve the system by substitution. - 4x-10y=5 4x+10y=5

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - x-z=5 y+z=2 x+z=9

Solve the problem. -Michaelʹs bank contains only nickels, dimes, and quarters. There are 65 coins in all, valued at $5.30. The number of nickels is 3 short of being three times the sum of the number of dimes and quarters. How many dimes are in the bank?

Evaluate the determinant. - $\left| \begin{array} { r r r } 8 & - 7 & 7 \\- 5 & - 7 & - 6 \\0 & 0 & 0\end{array} \right|$