Matrices & Determinants Questions and Answers

721 MODELING REAL LIFE In 2014 there were about MTR 7 billies cell phone subscribers in the world During the next 5 years the number of cell phone subscribers increased by about 3 each year See Example 3 a Write an expor ential nedel that represents the number of cell phone subscribers y in billions t years after 2014 Then estimate the number of cell phone subscribers in 2019 b Estimate when the number of cell phone 12 45

Construct the augmented matrix that corresponds to the following system of equations 5 8x 5 Answer y 4z3 x 3y 0 5x y 2 x 8z

Zor b eos 38 sin x sin 64 sin x tan 29

Consider the following matrix Step 1 of 3 Determine the order of C Answer How to enter your answer opens in new window 7 8 2 27 Let C 38 29 45 41 34 41 X

To solve equations with three variables start by Select one O a isolating X in one of the equations b adding all three equations together O c substituting trial values for the variables in one equation O d using elimination to get two equations with the same two variable in each

Use matrices to find the area of the figure below 55 5 square units 48 8 square units 58 5 square units 62 4 square units

Find the perimeter of the polygon The perimeter of the polygon is cm Simplify your answer Points 0 of 1 10 cm 9 a

tion 1 If A 2 0 1 then find the factorization of A 3

Let u 2 3 v 1 1 and A NOTE Give exact answers a Findu relative to the inner product on R generated by the matrix A 13 3 2 2 X b Find d u v relative to the inner product on R generated by the matrix A d u v 5 X

1 12 parking ramps are to be apportioned among 3 towns Fill in blanks States towns A C Number of 40000 people Standard divisor Standard quota Lower quota Upper quota 23000 B 57000 Total Surplus

Find the closest point to y in the subspace W spanned by v and V2 1 1 D V 0 4 y 3 1 1 19 1 Simplify your answer 3 1 1 The closest point to y in W is the vector 2 2 2 18

1 point Find the determinant of the matrix 2 2x 2 2x 4x 1 x 2x 20 12x M and use the adjoint method to find M det M M 1 7 10 6x 6 12x 2 6x 4 0 0 3 3x

Now pretend you are tossing a coin 7 times and take X to be the total number of tails that come up There are then 27 128 possible outcomes TTTTTTT HTTTTTT THTTTTT TTHTTTT TTTHTTT TTTTHTT TTTTTHT TTTTTTH Take X to be the total number of tails that come up The possible values of X are X HHHHHHT HHHHHTH HHHHTHH HHHTHHH HHTHHHH HTHHHHH THHHHHH HHHHHHH Separate the values with commas Now fill in the missing probabilities The other missing probabilities will appear when you correctly answer the question or press Do it P X 3 0 1 Check Clear Do it 2 3 4 5 6 7

6 5 4 3 2 1 1 2 3 4 a Based on the graph above estimate to one decimal place the average rate of change from x 1 to

Question 15 2 points Which of the following is equivalent to 4In x 3ln x In y O In X 13 y In 4x 3x y In x x y 10 X O In Question 16 2 points

A combination lock consists of a dial with 50 numbers on it To open the lock you turn the dial to the right until you reach a first number then to the left until you get to the second number then to the right again to the third number The numbers must be distinct How many different lock combinations are possible

Determine whether A is diagonalizable A 4 0

Solve the Leontief production equation for an economy with three sectors given the following 0 5 0 2 0 40 C 0 2 0 6 0 2 and d 60 0 1 0 0 4 90 X Do not round until the final answer Then round to the nearest ten as needed

Find the equation of a line with the given information f 13 15 and f 6 10 Use fractions in simplest form or integers when writing the equation of the line Write your answer in point slope form If your answer is a vertical line type your answer as a and if your answer is a horizontal line type your answer as y Write your answer in slope intercept form If your answer is a vertical line type your answer as a and if your answer is a horizontal line type your answer as y

Use matrices A 20 3 42 5 8 2 8 and B 7 6 403 7 6 4 1 to find 2A 1 3B 2A 1 3B

There is a Valentine s Day Sale at Coriale s Flowers on carnations and roses Matthew buys a total of 18 flowers and spends 78 00 Each carnation costs 3 and each rose costs 5 How many of each flower did Matthew buy

10 3 2 nd the leading principle submatrices of the matrix A 4 2 1 1 Tooo 0 1 0 2 0

A particular solution of x is a b 2tet 5 3et 2tet 5 2et C O d 2te t 5 3e t 2te 5 2e t 2te 5 3et 2tet 5 2et 2te t 5 3e t 2te t 5 2e t e none of the above 2 x 06

3 a 5 0 Given that the eigenvalue 3 is defective and the eigenvalue 5 is complete then a possible Jordan normal form of A is 310 0 03 0 0 00 0 0 0 5 30 0 03 0 0 00 50 0 0 0 5 31 0 0 03 1 0 00 5 1 000 5 10 0 0310 0 0 3 0 000 5 31 0 0 0300 00 50 0 5

3 Use algebra and trigonometry to solve the following system of 1291 equations Express the solutions so that 2 t 0 2T 12 p r 2cose r 2sin20 He

K rev Step 3 of 3 Using your answers to the previous steps polynomial division and the quadratic formula if necessary find all of the zeros of t polynomial Include multiples of the same zero where applicable Answer 2 Points Separate multiple answers with commas Keyboard

Gloria Newburg operates three self service gasoline stations in different parts of town On a certain day Station A sold 500 gal of premium 800 gal of super 1000 gal of regular gasoline and 700 gal of diesel fuel Station B sold 700 gal of premium 600 gal of super 1200 gal of regular gasoline and 400 gal of diesel fuel Station C sold 900 gal of premium 700 gal of super 1400 gal of regular gasoline and 800 gal of diesel fuel Assume that the price of gasoline was 3 20 gal for premium 2 98 gal for super 2 80 gal for regular and that diesel fuel sold for 3 10 gal Use matrix algebra to find the total revenue at each station Station A Station B Station C

The set that contains no elements is called the set natural numbers cardinal number empty or null

Consider the following 2 A No Find all eigenvalues of the matrix A Enter your answers as a comma separated list 3 1 Give bases for each of the corresponding eigenspaces Enter sqrt n for n smaller value span larger value span 1 sqrt 3 D Q 1 sqrt 3 1 Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ D Enter each matrix in the form row 1 row 2 where each row is a comma list 3 0 012 3 1 1

Find the best approximation to z by vectors of the form C V C V Z 3 15 0 1 V 3 0 1 2 V 6 1 12 3 The best approximation to z is Simplify your answer

4 1 6 Given matrix A2 1 6 show that A has an eigenvalue of 2 12 1 8 Then find a basis for the corresponding eigenspace

10 Given parallelogram PQRS with Aividing SR in the ratio 3 4 8 and C the points of trisection of QR and 7 the point of intersection of QA and SB show that 87 TS 4 9 P

6 find value of following matiz 1 2 3 4 a 6 23 a B such that the nvertible Show Transcribed Text Find value of A such that the following

Given the matrices B 5 5 4 1 5 3 find 3B 2C and C H 5 4 3 3 4 5

Use the Gram Schmidt Process to find an orthogonal basis for the column space of the matrix Use the Gram Schmidt Process found here to calculate your answer 011 1 11 011 1 5 0 5 303 2 0

Evaluate the function f x Inx at at x 4 461 Round to 3 decimal places You may use your calculator 1 148 0 498 O undefined 0 366 1 144

Solve the following system of linear equations using Gauss Seidel Metho 2x 3x 3x 5 x 2x x3 4 3x1 x 2x3 3

Show that I is a linear transformation by finding a matrix that implements the mapping Note that x x T X X XX x 5x 0 8x x x x4 are not vectors but are entries in vector

Solve the right triangle A 70 42 a 15 28 K B b C Simplify your answers Round to the nearest hundredth as needed Round to the nearest hundredth as needed

The table below gives the probability density of taffies in a bag Banana Chocolate Cherry 0 19 0 16 Taffy robability 0 21 Grape Vanilla 0 13 0 31 If a taffy is selected at random what is the probability that it is a vanilla or banana First enter the probability of vanilla P vanilla

Find a basis for the column space of A 5 0 A 11 11 1 1 3 5 2 0 1 1 1 31 2 P X Find a basis for the null space of AT for the given matrix Verify that every vector in col A is orthogonal to every vecto

2247 Reduce 1 1 2 to row echelon form 101 10 010 00 1 10 1 012 00 0 101 O 1 1 O O

Let A 45 9k For A to have 0 as an eigenvalue k must be

2w x y z 3 8w 7x 3y 5z 3 w 4x y z 6 w 3x 7y z 1 Use Cramer s rule to solve for y without solving for x z and w in the system

Find the matrix A of the quadratic form associated with the equation 6x 5xy 6y 12 0 4 6 2 5 2 5 6 Find the eigenvalues of A Enter your answers as a comma separated list 3 6 5 6 5 Find an orthogonal matrix P such that PTAP is diagonal Enter the matrix in the form row 1 row 2 where each row is a comma se

Solve each system of equations below using determinants 10 66 3x 3y 15 2r 4y 2 11 5x 6y 10 2x 3y 4 12 88 6x 2y 4 8 y 5 12 7x 4y 3x 2

Let A 3 19 9 025 0 1 0 Find det 44 T rk e Verilen A matrisi i in det 4A O 4 6 O 64 6 O 121 4 O 21 5 O 1 15

6 question 10 00 point s Conisder the system of equations x y z 2 x y z 3 x y z a 1 if a 0 then there is a unique solution II if a 1 then there is no solution III if a 1 then there are infinitely many solutions Which ones are true A III B I D E I and II II and III

Find u v ul v and d u v for the given inner product defined on R 1 1 1 v 5 4 5 u v U1V1 3U2V2 U3V3 U a u v b ul 3 c v d d u v X 52

Given f 1 x 2 1 for 1 2 R apply inverse SR 1 update rule to f 1 22 with 8 H 1 69 Xk 0 1 3 1 3 2 3 2 3 1 F None of them T 1 a 2 to obtain the next iteration H 1 a b d Find the value of c