Matrices & Determinants Questions and Answers

If A is a 3 x 3 matrix such that det A 3 then det A2 6 Select one O True O False

Determine if the relation defines y as a function of x 3 1 2 3 Yes this relation defines y as a function of x No this relation does not define y as a function of x

The following refer to the following data set 10 12 5 14 14 13 2 Find each of the following If a requested item does not exist enter DNE without qu marks What is the arithmetic mean of this data set Mean What is the median of this data set Median What is are the mode s of this data set Mode What is the range of this data set Range What is the midrange of this data set Midrange Use the given data to calculate the standard deviation x x

5 Diagonalize the matrix below Describe the eigenspace of each eigenvalue 3 2 4 1 2 2 7 1 3

U A I 01 Oll Olll IV Oll II V VII VI OIV OV III 1 Which region s represent set C OIV OV Olll OVI 2 Which region s represent set An C OIV OVII OV O VIII OVI Not enough information is provided 3 Which region s represent set A UBUC VIII B O VII O VIII Not enough information is provided OVII O VIII

ermine whether each statement is true or false If a statement is true give a reason or cite an appropriate statement from the text If a statement is false provide an example that shows statement is not true in all cases or cite an appropriate statement from the text a To find the determinant of a triangular matrix add the entries on the main diagonal O True the determinant of a triangular matrix is equal to the order of the matrix which is equal to the sum of the entries in the main diagonal O False the determinant of a triangular matrix is equal to the product of the entries in the main diagonal which may not be equal to the sum of the entries in the main diagonal O True the determinant of a triangular matrix is equal to the product of the entries in the main diagonal which is equal to the sum of the entries in the main diagonal O False the determinant of a triangular matrix is equal to the number of nonzero entries in the main diagonal which may not be equal to the sum of the entries in the main diagonal O False the determinant of a triangular matrix is equal to the order of the matrix which may not be equal to the sum of the entries in the main diagonal b To find the determinant of a matrix expand by cofactors in any row or column O False to find the determinant of a matrix expand by cofactors in any row but not in any column O False to find the determinant of a matrix expand by cofactors in only the first column O False to find the determinant of a matrix expand by cofactors in only the first row O True to find the determinant of a matrix expand by cofactors in any row or column O False to find the determinant of a matrix expand by cofactors in any column but not in any row c When expanding by cofactors you need not evaluate the cofactors of zero entries O True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be zero O True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be one O False in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be zero O True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be equal to the cofactor O False in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be equal to the cofactor

A graph of quadratic function y f x is shown below y f x CH 543211 J7 P T Y 2 3 4 12 3 4 5 X What is the solution set of the quadratic inequality f x 2 0 x x 3 XIXER x x 3

What is the solution set to the inequality 4x 3 2x 1 20 O x1 x 2 or X2 O x x 3 or x 1 XIXS 12 or xz 21

Identify the restrictions on the domain of f x Ox 5 Ox 5 Ox 2 X 5 X 2

An adult blue whale weighs 220 000 pounds An adult African Elephant weighs 5 5 tons How many times greater is the weight of the adult blue whale than the weight of the adult African elephant 17 86 SP times greater

The horizontal and vertical distance between 2 dots is 1 unit Find the area of the trapezoid by using a formula and then by counting the number of square units units2 Explain how you counted the number of square units

72 Show that no 2 x 2 matrices A and B exist that satisfy the matrix equation AB BA 1 9 0

A population of animals starts at 437 000 and grows continuously at 6 per year to 1 211 886 How long does it take to achieve this growth years E Round to the nearest whole number

10p Find solution of a system of linear equations with variables x X2 X3 X4 R x1 x2 x3 2x4 1 cx1 cx2 C cx c 1 x2 c 3 x3 2c 1 x c 5 x2 2x3 x4 5

b How many games can be stored if the average game size is 0 5 GB

Work required Use the inverse to solve the linear system z 2y z 2 2 2y z 4 z 2y z 2 H Z

Work required If possible write the column matrix b as a linear combination of the columns of A if column 1 is A column 2 is A2 and column 3 is As Parametrize your solution with 23 t t ER and then find the particular solution when t 1 Write your answer in these terms entering the coefficients in the blanks below If not possible type NS in each blank for the coefficients 1 2 4 A 1 0 2 b 2 0 1 3 Solution b A

A Ais O singular O invertible 26 O the identity matrix

Work required Determine whether x is a solution to the linear system Use a matrix equation and not row operations 1 2 1 A 1 1 2 x X 2 1 2 Select Select is is not 1 b 2 6 a solution to the system

If we have a linear system of two equations in three variables will this system necessarily have infinitalu Explain your answer Edit Formal

Work required Salve the homogeneous system of linear equations using Gauss Jordan Elimination or Gaussian Elimination Parametrize solutions if appropriate using zy t t E R Provide the solution for each variable in the blanks provided 2 2y 3z 0 23

An inverted index maps what to what Select one O O O O A individual terms to individual postings B individual terms to lists of postings C lists of terms to individual postings D lists of terms to lists of postings

Listen A high school band trip will require renting buses and trucks to transport no fewer than 150 students and 20 or more large instruments Each bus can accommodate 60 students plus 3 large instruments it costs 347 to rent Each truck can accommodate 15 students plus 7 large instruments and costs 195 to rent How many of each type of vehicle should be rented for the cost to be minimized Determine the minimum cost none of these 4 buses and 0 trucks 1388 O buses and 10 trucks 1950 1 buses and 4 trucks 1127 2 buses and 2 trucks 1084 Question 14 Bonus 0 33 points Listen An ice cream store sells two new flavors Fantasy and Excess Each barrel of Fantasy requires 6 pounds of nuts and 4 pounds of chocolate and has a profit of 540 Each

The sales S of a product have declined in recent years There were 202 million sold in 1984 and 1 2 million sold in 1994 Assume the sales are decreasing according to t exponential decay model S t Spe a Find the value k and write an exponential function that describes the number sold after time t in years since 1984 b Estimate the sales of the product in the year 2002 c In what year theoretically will only 1 of the product be sold a Rounded to six decimal places k

79

x 3 3x Select an answer and submit For keyboard navigation use the up down arrow keys to select an answer True or False The expression a b C d is undefined at x 3 True The value 3 satisfies the equation 3x 0 True The value 3 satisfies the equation X 3 0 False The value 3 does not satisfy the equation 3x 0 The correct value is 0 False The expression is defined for all values of X

3 Investigate the restrictions that should be applied to the domain of a cubic function so that it has an inverse Sketch a cubic function g x x 4x 2 Is this a one to one function Explain your answer If the domain is restricted between x a and x b where both a and b are finite real numbers the function becomes one to one Find the largest possible domain a b Use the idea from the cubic function and investigate the domain and range of all the inverse trigonometric functions Use the following as a guideline for investigating other trigonometric functions too Sketch the graph of y sin x Find the largest possible domain for which the inverse can exist Find the domain and range of sin x Sketch both y sin x and y sin 1 x within the restricted domain

Perform the following n 5 conversions on the array 75 80 99 100 50 0 numbers 0 75 corresponds to Roman numeral LXXV 50 X 10 X 10 V 5 Click bar to ope 1 numbers 1 80 corresponds to Roman numeral LXXX L 50 X 10 X 10 X 10 2 numbers 2 99 corresponds to Roman numeral XCIX XC 90 IX 9 3 numbers 3 100 corresponds to Roman numeral C 4 numbers 4 50 corresponds to Roman numeral L Return the array LXXV LXXX XCIX C L as the answer

Find the general solution of the system whose augmented matrix is given below 1 42 3 12 1 12 Select the correct choice below and if necessary fill in the answer box es to complete your choice O A O C X X is free X3 is free X 11 X 11 OB X X is free X3 OD The system has no solution

Choose h and k such that the system has a no solution b a unique solution and c many solutions X hx 5 2x 4x k F The system has no solutions only when h 2 and k 10 OG The system has no solutions only when h OH The system has no solutions only when k and k is any real number and h is any real number b Select the correct answer below and fill in the answer box es to complete your choice Type an integer or simplified fraction OA The system has a unique solution only when h OB The system has a unique solution only when k OC The system has a unique solution only when k OD The system has a unique solution only when h O E The system has a unique solution only when h OF The system has a unique solution only when h OG The system has a unique solution only when h and k is any real number and h is any real number and h is any real number and k and k and k is any real number and k

Determine if b is a linear combination of a a2 and a3 5 HH a 0 12 D 3 15 Choose the correct answer below O A Vector b is a linear combination of a a2 and a3 The pivots in the corresponding echelon matrix are in the first entry in the first column the second entry second column and the third entry in the third column B Vector b is a linear combination of a a2 and a3 The pivots in the corresponding echelon matrix are in the first entry in the first column and the second em the second column OC Vector b is not a linear combination of a a2 and a OD Vector b is a linear combination of a a2 and a3 The pivots in the corresponding echelon matrix are in the first entry in the first column the second entry second column and the third entry in the fourth column

et u 11 1 Let b and v 11 Show that h is in Span u v for all h and y How can it be shown that a vector b is in Span u v A Determine if the system containing u v and b is consistent If the system is inconsistent then b is in Span u v OB Determine if the system containing u v and b is consistent If the system is consistent b might be in Span u v C Determine if the system containing u v and b is consistent If the system is consistent then b is in Span u v OD Determine if the system containing u v and b is consistent If the system is consistent then b is not in Span u v h Find the augmented matrix ix u v b y

Let u 11 1 Let b and v h 11 1 h y Show that is in Span u v for all h and y How can it be shown that a vector b is in Span u v O A Determine if the system containing u v and b is consistent If the system is inconsistent then b is in Span u v OB Determine if the system containing u v and b is consistent If the system is consistent b might be in Span u v C Determine if the system containing u v and b is consistent If the system is consistent then b is in Span u v Determine if the system containing u v and b is consistent If the system is consistent then b is not in Span u v OD Find the augmented matrix x u v b

Write a vector equation that is equivalent to the given system of equations x 3x3 0 5x 8X2 X3 0 X 3x 8x3 0 Choose the correct answer below O A 1 O C B 8 X3 O O O 04 0 1 O B 0 19 X X 0 1 3 8 X3 H 3 B BH 3 0

The augmented matrix of a linear system has been reduced by row operations to the form shown Continue the appropriate row operations and describe the solution set of the original system GILER Select the correct choice below and if necessary fill in the answer boxes to complete your choice A The solution set has exactly one element 0 Type integers or simplified fractions OB The solution set has infintely many elements C The solution set is empty 18 00 00 01

Find an equation involving g h and k that makes this augmented matrix correspond to a consistent system 1 3 79 0 5 12 h 3 4 9 k What equation must be satisfied for the augmented matrix to correspond to a consistent system Select the correct choice below and fill in the answer box to comp your choice Simplify your answer OA 3g h k OB 3g h k O c 3g h k OD 3g h k

the statement below is true or false Justify the answer Two matrices are row equivalent if they have the same number of rows Choose the correct answer below ACCEN OA The statement is false Two matrices are row equivalent if the equation corresponding to the first row of the first matrix is equivalent to the equation corresponding to the first row of the second matrix the equation corresponding to the second row of the first matrix is equivalent to the equation correspon to the second row of the second matrix and so forth OB The statement is false Two matrices are row equivalent there exists a sequence of elementary row operations that transforms one matrix into the other C The statement is true It is the definition of row equivalence OD The statement is true Two matrices are row equivalent if there exists can only occur if the matrices have the same number of rows sequence of elementary row operations that transforms one matrix into the other T

FIND THE SLOPE OF THE LINEAR FUNCTION IN EACH BUL SLOPE 987 59 6 327 9 8 7 6 5 4 3 2 1 123456789 2 WN V 6799 in 6 7 8 SLOPE x

4x 6y ax 2y 3 Consider the system of linear equations a Write the system as an augmented matrix 1 b Multiply the second row by 3 c For what value s of a is the system inconsistent

Show that Every square matrix A can be expressed as the sum of a symmetric matrix and a skew symmetric matrix

3 Determine the unknown length Round to the nearest hundredth 20 15 m

A sequence has nth term a cos 90n n 1 a Find the order of the sequence b Find a

3 3 6x 4 A 6x C 4x B 3x D Tx Write each expression in exponential form 4 3n A 7n C 6n 3 B 3n 4 D 7n 5 5 Vb A b C 26 23 B b D b

1 Jake is observing the population growth of insects He started with 24 insects and the population triples every day Use x to represent the of days and y to represent the population of insects Write an equation to represent the scenario 2 Tell if each equation represents exponential growth exponential decay or neither and why a f t b P 22 1 76 c V 0 45 d W 3 2 x e g x 4 2 3

What is the GCF of the expression below that could be use to rewrite the polynomial in factored form 24p 30p 3p4 6p4 24p

A 2 Find the determinant of given matrix using cofactor expansion 1 0 1 0 2 5 0 0 0 5 0 0 COLO 1 054

4 Given the following matrices compute the indicate 3 2 1 1 0 0 A 4 L2 a ATBT b CIn 5 B 2 1 3 1 01 2 21 C 3 4

3 Given the following matrices compute A B 2 O 11 1 0 1 3 A 5 LO 3 B 1 2

Write the row operations you would need in order to finish row reducing this matrix and perform the operations 1 0 4 0 1 0 00 3 7 3 15

Perform the indicated operation 1 2 5 3 4 8 X 0 10 14 6