Solve the problem. -In matrix C, a coffee shop records the cost to produce a cup of coffee and the cost to produce a cup of hot chocolate. Matrix P contains the selling prices to the customer. $\begin{array} { c } \text { coffee chocolate } \\ C = \left[ \begin{array} { l l } \$ 0.93 & \$ 0.86 \\ \$ 1.21 & \$ 1.11 \\ \$ 1.51 & \$ 1.41 \end{array} \right] \text { Small Large } \quad \text { coffee chocolate } \\ \text { Medium } ; P = \left[ \begin{array} { l l } \$ 3.00 & \$ 2.40 \\ \$ 3.75 & \$ 3.15 \\ \$ 4.40 & \$ 3.90 \end{array} \right] \text { Sedium } \\ \text { Large } \end{array}$ a. Compute P - C and interpret its meaning. b.If the tax rate in a certain city is 6%, use scalar multiplication to find a matrix F that gives the final Price to the customer (including sales tax) for both beverages for each size. Round each entry to the Nearest cent.

A) a. $P - C = \left[ \begin{array} { l l } \$ 2.07 & \$ 1.54 \\ \$ 2.54 & \$ 2.04 \\ \$ 2.89 & \$ 2.49 \end{array} \right]$ ; this represents the profit that the store makes for both beverages for । size. b. $F = \left[ \begin{array} { l l } \$ 0.18 & \$ 0.14 \\ \$ 0.23 & \$ 0.19 \\ \$ 0.26 & \$ 0.23 \end{array} \right]$ B) a. $P - C = \left[ \begin{array} { l l } \$ 2.07 & \$ 1.54 \\ \$ 2.54 & \$ 2.04 \\ \$ 2.89 & \$ 2.49 \end{array} \right]$ ; this represents the profit that the store makes for both beverages for । size. b. $F = \left[ \begin{array} { l l } \$ 2.19 & \$ 1.63 \\ \$ 2.69 & \$ 2.16 \\ \$ 3.06 & \$ 2.64 \end{array} \right]$ C) a. $P - C = \left[ \begin{array} { l l } \$ 2.07 & \$ 1.54 \\ \$ 2.54 & \$ 2.04 \\ \$ 2.89 & \$ 2.49 \end{array} \right]$ ; this represents the profit that the store makes for both beverages for । size. b. $F = \left[ \begin{array} { l l } \$ 3.18 & \$ 2.54 \\ \$ 3.98 & \$ 3.34 \\ \$ 4.66 & \$ 4.13 \end{array} \right]$ D) a. $P - C = \left[ \begin{array} { l l } \$ 3.93 & \$ 3.26 \\ \$ 4.96 & \$ 4.26 \\ \$ 5.91 & \$ 5.31 \end{array} \right]$ ; this represents the profit that the store makes for both beverages for । size. b. $F = \left[ \begin{array} { l l } \$ 3.18 & \$ 2.54 \\ \$ 3.98 & \$ 3.34 \\ \$ 4.66 & \$ 4.13 \end{array} \right]$ A) a. $P - C = \left[ \begin{array} { l l } \$ 2.07 & \$ 1.54 \\ \$ 2.54 & \$ 2.04 \\ \$ 2.89 & \$ 2.49 \end{array} \right]$ ; this represents the profit that the store makes for both beverages for । size. b. $F = \left[ \begin{array} { l l } \$ 0.18 & \$ 0.14 \\ \$ 0.23 & \$ 0.19 \\ \$ 0.26 & \$ 0.23 \end{array} \right]$ B) a. $P - C = \left[ \begin{array} { l l } \$ 2.07 & \$ 1.54 \\ \$ 2.54 & \$ 2.04 \\ \$ 2.89 & \$ 2.49 \end{array} \right]$ ; this represents the profit that the store makes for both beverages for । size. b. $F = \left[ \begin{array} { l l } \$ 2.19 & \$ 1.63 \\ \$ 2.69 & \$ 2.16 \\ \$ 3.06 & \$ 2.64 \end{array} \right]$ C) a. $P - C = \left[ \begin{array} { l l } \$ 2.07 & \$ 1.54 \\ \$ 2.54 & \$ 2.04 \\ \$ 2.89 & \$ 2.49 \end{array} \right]$ ; this represents the profit that the store makes for both beverages for । size. b. $F = \left[ \begin{array} { l l } \$ 3.18 & \$ 2.54 \\ \$ 3.98 & \$ 3.34 \\ \$ 4.66 & \$ 4.13 \end{array} \right]$ D) a. $P - C = \left[ \begin{array} { l l } \$ 3.93 & \$ 3.26 \\ \$ 4.96 & \$ 4.26 \\ \$ 5.91 & \$ 5.31 \end{array} \right]$ ; this represents the profit that the store makes for both beverages for । size. b. $F = \left[ \begin{array} { l l } \$ 3.18 & \$ 2.54 \\ \$ 3.98 & \$ 3.34 \\ \$ 4.66 & \$ 4.13 \end{array} \right]$

Exam 6: Matrices and Determinants and Applications

Write the system of equations as a matrix equation of the form AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants. - -5x-8y+9z=16 2x-z=5 -7y+z=8

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Question 141

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false? A system of linear equations in three variables may have exactly two solutions.

(True/False)

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Question 142

Solve the problem. -Danielle stayed in three different cities (Washington, D.C., Atlanta, Georgia, and Dallas, Texas) for a total of 22 nights. She spent twice as many nights in Dallas as she did in Washington. The total Cost for 22 nights (excluding tax) was $3,100. Determine the number of nights that she spent in each city. City Cost per Night Washington \ 100 Atlanta \ 175 Dallas \ 150

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Question 143

Use a calculator to approximate the reduced row-echelon form of the augmented matrix representing the given system. Give the solution set where x, y, and z are rounded to 2 decimal places. - 0.52x-3.79y-4.67z =9.15 0.03x+0.06y+0.13z =0.53 0.974x+0.813y+0.419z =0.189

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Question 144

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Assume that traffic flows freely through intersections A, B, and C. The values $x _ { 1 } , x _ { 2 } , x _ { 3 }$ , and all other numbers in the figure represent flow rates in vehicles per hour. $Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Assume that traffic flows freely through intersections A, B, and C. The values x _ { 1 } , x _ { 2 } , x _ { 3 } , and all other numbers in the figure represent flow rates in vehicles per hour. a. Write an equation representing equal flow into and out of intersection A. b. Write an equation representing equal flow into and out of intersection B. c. Write an equation representing equal flow into and out of intersection C. d. Write the system of equations from parts (a)-(c) in standard form. e. Write the reduced row-echelon form of the augmented matrix representing the system of equations from part (d). f. If the flow rate between intersections A and C is 120 vehicles per hour, determine the flow rates x _ { 1 } and x _ { 2 } g. If the flow rate between intersections A and C is between 150 and 240 vehicles per hour, inclusive, determine the flow rates x _ { 1 } \text { and } x _ { 2 }$ a. Write an equation representing equal flow into and out of intersection A. b. Write an equation representing equal flow into and out of intersection B. c. Write an equation representing equal flow into and out of intersection C. d. Write the system of equations from parts (a)-(c) in standard form. e. Write the reduced row-echelon form of the augmented matrix representing the system of equations from part (d). f. If the flow rate between intersections A and C is 120 vehicles per hour, determine the flow rates $x _ { 1 }$ and $x _ { 2 }$ g. If the flow rate between intersections A and C is between 150 and 240 vehicles per hour, inclusive, determine the flow rates $x _ { 1 } \text { and } x _ { 2 }$

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Question 145

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false? A system of linear equations in three variables may have infinitely many solutions.

(True/False)

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Question 146

Choose the one alternative that best completes the statement or answers the question. Write the augmented matrix for the given system. - 7x+9 =-7z -4x+4z =-8-6y -3x-7y+9z =2

(Multiple Choice)

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Question 147

Solve the problem. -A student researches the cost for three cell phone plans. Matrix C contains the cost per text message and the cost per minute over the maximum number of minutes allowed in each plan. Matrix N Represents the number of text messages and number of minutes over the maximum for 3 months. $\quad\text { Cost/text } \text { Cost/min }$ $C=\left[\begin{array}{cc|l}\$ 0.20 & \$ 0.35 & \text { Plan A } \\\$ 0 & \$ 0.35 & \text { Plan B } \\\$ 0.15 & \$ 0 & \text { Plan C }\end{array}\right.$ Month 1 Month 2 Month 3 Nequals open bracket 27 60 25 105 27 0 close bracket Number of texts Minutes over Find the product $C N$ and interpret its meaning.

(Multiple Choice)

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Question 148

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the of a matrix is $p \times q$ , then p represents the number of and q represents the number of .

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Question 149

Given the matrices A and B, solve for X. - $2 X = 2 A - B$ $A = \left[ \begin{array} { r r } - 6 & - 4 \\ 6 & 4 \end{array} \right]$ and $B = \left[ \begin{array} { r r } - 8 & - 18 \\ 6 & 16 \end{array} \right]$

(Multiple Choice)

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Question 150

Determine if the matrix is in row-echelon form. - $\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 0 & 2 \\0 & 1 & 0 & 0 & 4 \\0 & 0 & - 1 & 0 & 9 \\0 & 0 & 0 & 1 & - 6\end{array} \right]$

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Question 151

Solve the problem. -In matrix C, a coffee shop records the cost to produce a cup of coffee and the cost to produce a cup of hot chocolate. Matrix P contains the selling prices to the customer. coffee chocolate C= \ 0.93 \ 0.86 \ 1.21 \ 1.11 \ 1.51 \ 1.41 Small Large coffee chocolate Medium ;P= \ 3.00 \ 2.40 \ 3.75 \ 3.15 \ 4.40 \ 3.90 Sedium Large a. Compute P - C and interpret its meaning. b.If the tax rate in a certain city is 6%, use scalar multiplication to find a matrix F that gives the final Price to the customer (including sales tax) for both beverages for each size. Round each entry to the Nearest cent.

(Multiple Choice)

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Question 152

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { r r r } - 3 & - 8 & - 2 \\5 & 2 & 5\end{array} \right]$

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Question 153

The solution set to a system of dependent equations is given. Write three ordered triples that are solutions to the system. Answers may vary. - $\left\{ \left( \frac { 6 - 4 y - 15 z } { 3 } , y , z \right) \mid y \right.$ and $z$ are any real numbers $\}$

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Question 154

Showing 141 - 154 of 154

Write the system of equations as a matrix equation of the form AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants. - -5x-8y+9z=16 2x-z=5 -7y+z=8

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false? A system of linear equations in three variables may have exactly two solutions.

Use a calculator to approximate the reduced row-echelon form of the augmented matrix representing the given system. Give the solution set where x, y, and z are rounded to 2 decimal places. - 0.52x-3.79y-4.67z =9.15 0.03x+0.06y+0.13z =0.53 0.974x+0.813y+0.419z =0.189

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false? A system of linear equations in three variables may have infinitely many solutions.

Choose the one alternative that best completes the statement or answers the question. Write the augmented matrix for the given system. - 7x+9 =-7z -4x+4z =-8-6y -3x-7y+9z =2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the of a matrix is $p \times q$ , then p represents the number of and q represents the number of .

Given the matrices A and B, solve for X. - $2 X = 2 A - B$ $A = \left[ \begin{array} { r r } - 6 & - 4 \\ 6 & 4 \end{array} \right]$ and $B = \left[ \begin{array} { r r } - 8 & - 18 \\ 6 & 16 \end{array} \right]$

Determine if the matrix is in row-echelon form. - $\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 0 & 2 \\0 & 1 & 0 & 0 & 4 \\0 & 0 & - 1 & 0 & 9 \\0 & 0 & 0 & 1 & - 6\end{array} \right]$

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { r r r } - 3 & - 8 & - 2 \\5 & 2 & 5\end{array} \right]$

The solution set to a system of dependent equations is given. Write three ordered triples that are solutions to the system. Answers may vary. - $\left\{ \left( \frac { 6 - 4 y - 15 z } { 3 } , y , z \right) \mid y \right.$ and $z$ are any real numbers $\}$

Equations and Inequalities

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Exam 6: Matrices and Determinants and Applications

Write the system of equations as a matrix equation of the form AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants. - -5x-8y+9z=16 2x-z=5 -7y+z=8

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false? A system of linear equations in three variables may have exactly two solutions.

Use a calculator to approximate the reduced row-echelon form of the augmented matrix representing the given system. Give the solution set where x, y, and z are rounded to 2 decimal places. - 0.52x-3.79y-4.67z =9.15 0.03x+0.06y+0.13z =0.53 0.974x+0.813y+0.419z =0.189

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false? A system of linear equations in three variables may have infinitely many solutions.

Choose the one alternative that best completes the statement or answers the question. Write the augmented matrix for the given system. - 7x+9 =-7z -4x+4z =-8-6y -3x-7y+9z =2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the ________of a matrix is p×qp \times qp×q , then p represents the number of________ and q represents the number of .

Given the matrices A and B, solve for X. - 2X=2A−B2 X = 2 A - B2X=2A−B A=[−6−464]A = \left[ \begin{array} { r r } - 6 & - 4 \\ 6 & 4 \end{array} \right]A=[−66​−44​] and B=[−8−18616]B = \left[ \begin{array} { r r } - 8 & - 18 \\ 6 & 16 \end{array} \right]B=[−86​−1816​]

Determine if the matrix is in row-echelon form. - [100020100400−1090001−6]\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 0 & 2 \\0 & 1 & 0 & 0 & 4 \\0 & 0 & - 1 & 0 & 9 \\0 & 0 & 0 & 1 & - 6\end{array} \right]​1000​0100​00−10​0001​249−6​​

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - [−3−8−2525]\left[ \begin{array} { r r r } - 3 & - 8 & - 2 \\5 & 2 & 5\end{array} \right][−35​−82​−25​]

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Filters

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the of a matrix is $p \times q$ , then p represents the number of and q represents the number of .

Given the matrices A and B, solve for X. - $2 X = 2 A - B$ $A = \left[ \begin{array} { r r } - 6 & - 4 \\ 6 & 4 \end{array} \right]$ and $B = \left[ \begin{array} { r r } - 8 & - 18 \\ 6 & 16 \end{array} \right]$

Determine if the matrix is in row-echelon form. - $\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 0 & 2 \\0 & 1 & 0 & 0 & 4 \\0 & 0 & - 1 & 0 & 9 \\0 & 0 & 0 & 1 & - 6\end{array} \right]$

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { r r r } - 3 & - 8 & - 2 \\5 & 2 & 5\end{array} \right]$