Matrices & Determinants Questions and Answers

Math gebra 1 M 7 Properties of matrices R 4 If F 8 6 6 1 5

Simplify the complex fraction 40 3 40x 3 5x 5

Question 9 1 point Which type of friction is usually greater O both are equal sliding friction O static friction Question 10 1 point I push on a box with 200 N of force and it accelerates The force of friction is O equal to 200 N O zero less than 200 N more than 200 N

3 A 0 Find the inverse matrix A 00 0 0 1 0 2 0 1 0 0 2 1 0 0 0 1 1 00 0 0 1 0 10 0 1 0 03 1 1 0 0

One of the key determinants of economic growth is access to capital Using 54 variables to create an index of 1 7 with 7 been best possible access to capital Milken Institue ranked the following as the top ten nations although technically Hong Kong is not a nation by the ability of their entrepreneurs to gain access to capital Country Index Hong Kong Netherland U K 5 59 5 07 5 34 a 0 28 3 25 o 0 28 Singapore Switzerland U S 3 32 a 0 43 5 94 o 0 27 5 34 o 0 58 5 04 5 47 5 23 5 39 Australia Finland Germany Denmark 5 92 5 01 Find the mean of the indices of the top ten nations What is the standard deviation of these data 5 27 5 43

5 Rotate the points D 1 by 45 around the point po Define the affine map needed here in terms of a matrix and a poi Po P1 13 P2 P3

The climate dynamics of the South Asian monsoon are best described as Ohigh pressure cell builds on land during the winter bringing precipitation to South Asia O low pressure cell builds on land during the summer bringing precipitation to South Asia Olow pressure cell builds on land during the winter bringing rain from the Indian Ocean high pressure cell builds on land during the summer bringing rain from the Indian Ocean

Maximize p 10x 10y 15z subject to x y z 14 2x 2y z 15 y z 3 x 0 y 0 z 0 Determine p x y z

The carpet cleaning costs for a local company are shown in the table and can be modeled by a linear function Find the rate of change and initial value for this relationship and explain what they mean in this context Rooms cleaned Cost 1 2 3 4 125 175 225 275 Rate of change The rate of change is carpet cleaning company charges an additional each room they clean Initial value The initial value of the function is company charges a flat fee of of rooms they clean Equation y mx b per room The for The regardless of the number

cos 2u tan 2u Need Help Read It 3 Points Use the given conditions to find the exact values of sin 2u cos 2u and tan 2u using the double angle formulas cos u 15 17 2 U T sin 2u DETAILS LARPCALCLIM5 5 5 020

S and T are mutually exclusive events Find P S or T P S 5 2 P T 1 2 12 P S or T Round to three decimal places as needed

4 The following graph can be described using an equation of the form y Asin x C Determine the values of A and C Show how you arrived at your answers 3 2 30 1 2 6 1 2 30 3 2 6

Exercise 5 Convert each of the following common radian angles into degrees 5T a 0 6 os 3 b 8 3n 2 c 0 3 4

Calculate the determinant D ab c d Tabl

Solve the following system of equations using Cramer s rule if it is applicable If Cramer s rule is not applicable say so 2x 2y 22 6x 5y 11 Select the correct choice below and if necessary fill in the answer boxes to complete your choice O A Cramer s rule is applicable The solution is x Simplify your answer OB Cramer s rule is not applicable y

Solve the system of equations using Cramer s Rule if it is applicable 6x 18 3X 3x 3y 0 Select the correct choice below and fill in any answer boxes within your choice O A Cramer s Rule is applicable The solution is x Simplify your answers OB Cramer s Rule is not applicable and y

Find the value of the determinant 4 55 4 60 1 32 4 55 4 60 1 32

Find the value of the determinant 55 1 1 3 2 133

Complete the sentence below by replacing with an appropriate value Using Cramer s Rule the value of x that satisfies the system of equations Choose the correct answer below 52 31 2 1 3 2x 3y 5 x 4y 3 is x O 2 1 4 ical 5 3 4 O

Write the system of equations corresponding to the augmented matrix Then perform the row operations R 6r r and R3 4r r3 on the given augmented matrix Which of the following is the system of equations corresponding to the augmented matrix SOA x 2y 2z 3w 6x 2y 8z6w 4x 2y 6z 6w O C CITE x 2y 2 3 6x 2y 8 6 4x 2y 6 6 O B O D x 2y 2z 3 0 6x 2y 8z 6 0 4x 2y 6z 6 0 x 2y 2z 3 6x 2y 8z 6 4x 2y 6z 6 Save 1 2 23 6 2 8 6 4 26 6

Find real numbers a b and c so that the graph of the function y ax bx c contains the points 1 4 2 9 and 0 3 Select the correct choice below and fill in any answer boxes within your choice OA The solution is a b and c Type integers or simplified fractions OB There are infinitely many solutions Using ordered triplets they can be expressed as a b c a Simplify your answers Type expressions using c as the variable as needed OC There are infinitely many solutions Using ordered triplets they can be expressed as a b c a Simplify your answer Type an expression using b and c as the variables as needed OD There is no solution b cany real number b any real number cany real numbe

Below is the table for the function f x x 2 6 9 12 16 y 3 4 7 13 15 Choose the one table below which is the inverse function f x O C x Y x 16 Y 15 83 Y eg 2 6 9 1 3 1 4 1 7 1 3 3 12 9 6 13 7 4 1 4 1 7 4 7 12 16 1 13 1 15 2 23 1 13 1 15 13 15

6 ts TB MC Qu 04 76 Algo The Wilson Company pur The Wilson Company purchased 33 000 of merchandise from th The company uses the perpetual Inventory system Which of the Company Consider the effects of both business events

2 Test the following series for convergence a 9 points 106n cos n sin n 13n n n 2

If 10 percent of 50 percent of a number is 30 less than one quarter of the number what is the number O 120 O 160 O 150 100

Stefan is conducting an experiment to find the level of pollution in the air He found that there are about 3 billion dust particles in one square meter of space What is the approximate weight of 3 billion dust particles if one dust particle weighs 4 66 10 12 grams O 1 4 x 10 grams O 1 4 x 101 grams O 1 4 x 102 grams O 1 4 x 10 grams O 1 4 grams

Question 45 of 60 What is the solution of the given expression O 2 401 O 49 1 49 O 2 400 O 2 401

Solve for x 15x x 2 x 2 or x 1 O or x x W L x 1 3 or x 1 Worth more or less including zero depending on your

com math algebra 1 weighted averag 9 Search topics and skills Assessment Math A LE

Write down the system of equations corresponding to the augmented matrix shown below 4 41 3 9 Provide your answer below 9 5 7 3 Use the variables z y and z for the first second and third variables of the system respectively Note Write an equation in each answer field and do not solve the system

Find the total year costs for 5 years 10 years and 15 years for purchasing and renting a house Then compare your answers to those in the following table Length of Time Purchase Home Rent Home 5 years 10 years 15 years 78 559 20 54 900 00 127 118 40 115 200 00 175 677 60 180 900 00 Purchase Home Total 5 year cost 30 000 00 5 x 12 x 809 32 78 559 20 Total 10 year cost 30 000 00 10 x 12 x 809 32 127 118 40 Total 15 year cost 30 000 00 15 x 12 x 809 32 175 677 60 Rent Home Total 5 year cost 4 x 12 x 900 1 x 12 x 975 54 900 Total 10 year cost 4 x 12 x 900 4 x 12 x 975 2 x 12 x 1050 115 200 Total 15 year cost 4 x 12 x 900 4 x 12 x 975 4 x 12 x 1050 3 x 12 x 1125 180 1900 Recall the pros and cons of buying a house and which conditions make it better to to purchase a home Also think about the pros and cons of renting a house and which conditions make it better to rent Use this information along with the total costs you found to answer the following prompts Make sure to write your answer in complete sentences Does renting or purchasing makes the most sense for the Bainters if they live in the house 1 year 5 years 10 years 15 years rom home Use mathematical

9 Exercise 5 3A Algo Allocating product cost between cost of goods sold and ending Inventory multiple purchases LO 5 1 4 06 Cortez Company sells chairs that are used at computer stations Its beginning Inventory of chairs was 150 units at 70 per unit During the year Cortez made two batch purchases of this chair The first was a 114 unit purchase at 79 per unit the second was a 232 unit purchase at 84 per unit During the period It sold 284 chairs Required Determine the amount of product costs that would be allocated to cost of goods sold and ending Inventory assuming that Cortez uses a FIFO b LIFO c Weighted average Complete this question by entering your answers in the tabs below Req A1 Req A2 FIFO Req B1 Determine the amount of product costs that would be allocated to cost of goods sold assuming that Cortez uses FIFO Cost of Goods So Units Req B2 E Unit Cost Reg C

A botanist can purchase plant food of four different types I II III and IV Each food comes in the same size bag and the following table summarizes the number of grams of each of three nutrients that each bag contains Food grams I II III IV Nutrient A 5 5 10 5 Nutrient B 10 5 30 10 Nutrient C 5 15 10 25 The botanist wants to use a food that has these nutrients in a different proportion and determines that he will need a total of 9 500 g of A 21 500 g of B and 16 500 g of C Find the number of bags of each type of food that should be ordered Let x R Type I bags y Type II bags z Type III bags and w Type IV bags If there are infinitely many solutions express your answers in terms of w as in Example 3

Exercise 4 7 13 Let P 1 2 3 be a point in R Let L be the line through the point Po 1 4 5 with HE direction vector d closest to P Find the shortest distance from P to L and find the point Q on L that is

What is the volume of the space between the cylinder and the cone 108 cubic units O90 cubic units O 30x cubic units O 120 cubic units 60x cubic units D 3 units

Let g x 3 x Let T P R P R and U P2 R R be the linear transformations respectively defined by T f x f x g x 2f x and U a bx cr a b c a b Let 3 and y be the standard ordered bases of P2 R and R respectively Show Transcribed Text O a Compute U T s and UT directly Then use Theorem 2 11 to verify your result b Let h z 3 2x x Compute h r and U h x Then use U from a and Theorem 2 14 to verify your result

5 12 points For each of the following subspaces WC R find a basis and determine the dimension a W N A where b Wspan S where 1 1 2 A 1 1 2 2 3 5 S 101 2 1 1 1 1 0 1 2 1

Given the equation AX B 4X 3C where A C Find X X 3 9 9 1 8 47 6 7 7 5 0 07 3 1 2 EH E 14 11 3 B 2 10 7 4 2 5 8 5 6

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the Gauss Jordan method if the inverse doesn t exist z 1 14 y 4z 3 y x 2x 4y What is the inverse of the coefficient matrix OA The inverse matrix is Type a matrix using an integer or simplified fraction for each matrix element Do not factor out a scalar multiple OB There is no inverse of the given matrix Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution of the system is Simplify your answer Type an ordered triple B There are infinitely many solutions The solution is z where z is any real number Use integers or fractions for any nurbbers in the expression OC There is no solution

Which number d forces a row exchange and what is the triangular system not singular for that d Which d makes this system singular no third pivot 2x 5y z 0 4x dy z 2 V Z 3

A bakery sells three types of cakes each requiring the amounts of the basic ingredients shown in the following matrix Type of Cake Flour in cups Sugar in cups Eggs III 2 4 4 2 1 2 2 1 3 To fill its daily orders for these three kinds of cakes the bakery uses 98 cups of flour 48 cups of sugar and 61 eggs Complete parts a through c below Ingredient a Write a 3x1 matrix for the amounts used daily The matrix is OA 98 48 61 b Let the number of daily orders for cakes be a 3x1 matrix X with entries x x and x3 Write a matrix equation that can be solved for X using the given matrix and the matrix from part a 4 4 2 2 12 2 3 OB 24 4 2 12 2 1 3

Suppose that A and B are invertible 2 x 2 matrices such that det A 4 and det B 2 Let x ER be a scalar such that det x A B What are the possible values of x x or

If f x 1 and n x X compare f x and n x units the graph of f x 1 x 6 The graph of n x is a translation of fill in the blanks to

The drama club had x cars at 5 each and can be used to repre

Red Bookstore wants to ship books from its warehouses in Brooklyn and Queens to its stores one on Long Island and one in Manhattan Its warehouse in Brooklyn has 1 000 books an its warehouse in Queens has 2 000 Each store orders 1 500 books It costs 5 to ship each book from Brooklyn to Long Island and 1 to ship each book from Brooklyn to Manhattan costs 4 to ship each book from Queens to Long Island and 2 to ship each book from Queens to Manhattan a If Red has a transportation budget of 8 760 and is willing to spend all of it how many books should Red ship from each warehouse to each store in order to fill all the orders Assume Red spends the entire transportation budget Brooklyn to Long Island Brooklyn to Manhattan Queens to Long Island Queens to Manhattan b Is there a way of doing this for less money Yes books books books books

Write an explicit formula for the sequence The first five terms of the sequence are 4 2 1 n 1 1 4 2 C an 2 n 1 A an Select one OA B B an n 1 4 1 1 n 1 D an 6

pick three points and use a cros product to find the area of the triangle they are the vertices of

Calculate det C100 Show your work Hint use the identity det M det M No computational aid should be necessary 01 201 7 0 4 0

Ceruly Lesson 6 8 Volume and Surface Area 5 Step 1 of 1 me of a rectangular pyramid with a length of 6 cm a w

x 13x 15 10v x 3 15x 3x 12 5x 3 2x 1 9 x 9 x 3x 1 3x 1 2x 3 2x 3 x 14x 45 5x 3 3x 1 x 3 x 2 9 X x 9 x 5 X 8 x 5 x 3x 10 6x 1 x 3x 40 5x 1 5x 1 x 12x 45 10x x 3 X 8 x 5 5y 12y 4 5y 12y 4 x 6 x 6 x 3 x 3 x 9x 10 3x 1 2x 3 3 4x 15x 2x 13x 15 2x 13x 15 5x 4 x 1 2x 3 x 5 25x 36 5x 3 2x 1 4x 9 x 3x 13 3x 1 9x 1 3 5x 1 3x 5x x 4 5x x 4 x 3x 28 x 15 x 3 x 13x 40 x 8 x 5 x 6x 5 2x 5 5x 2 5x 1 5x 6 x 3x 40 6x 9x 1 9x 6x 1 5x 4 x 1 10x 29x 10 3x 13x 15 x 7 x 4 5 x x 2 x 81 x 1 x 10 x 100 3 5x 4 x 1 x 5x 6 5x 6 5x 6 3x 1 y 2 5y 2