Linear Algebra Questions and Answers

Solve the equation for s y sx m

Let T M 2 R be a linear transformation for which 4 18 12 11 1 16 0 2 1 a b Find 7 33 and 7 06 T 53 C 2 51 1 3 a b Tab d 0 11 8

Find either the nullity or the rank of T and then use the Rank Theorem to find the other p 0 p 7 nullity 7 rank T T P R defined by T p x

Verify that S and T are inverses S P P defined by S a bx 4a b 2ax and T P P defined by T a bx b 2 a 2b x We must verify that So T So 7 a bx To S a bx 1p and To S 1p Thus S o T a bx To S a bx for any a bx EP so both compositions are the identity and we are c

Consider the following linear transformation T P R defined by T p x Find the nullity of T nullity T p 0 p 3 Determine if the linear transformation is one to one O one to one O not one to one Determine if the linear transformation is onto Onto because the range of T is exactly the codomain O Onto because T is one to one and the kernel is trivial O Not onto because T is not one to one and the domain and codomain have the different dimer O Not onto because T is not one to one and the kernel is nontrivial

Define linear transformations S P P and T P P by S a bx a a b x 5bx and T a bx cx2 b 5cx Compute So T 8 5x x2 and S o T a bx cx So T 8 5x x So T a bx cx Can you compute To S a bx If so compute it If an answer does not exist enter DNE To S a bx

Consider the transformation T M 2 M22 defined by T A AB where B Find basis for the kernel of the linear transformation T Enter your answers as a comma separated list Enter each matrix in the form row 1 row 2 where each row is a comma separated lis ker T Find either the nullity or the rank of T and then use the Rank Theorem to find the other nullity T rank 7

Determine whether V and W are isomorphic If they are give an explicit isomorphism T V W V P W p x in P3 p 0 0 O V and W are isomorphic and T ax bx cx a bx cx is an explicit isomorphism T V W O V and W are isomorphic and T a bx cx 1 ax bx cx3 is an explicit isomorphism T V W O V and W are isomorphic and T a bx cx ax bx cx is an explicit isomorphism T V W O V and W are isomorphic and T 1 ax bx cx a bx cx is an explicit isomorphism T V W O V and W are not isomorphic

Let T P P be the linear transformation defined by T p x xp x Find bases for the kernel and range of the linear transformation T Enter your answers as comma separated lists kernel range State the nullity and rank of T and verify the Rank Theorem nullity 7 rank 7

Let T R2 P be a linear transformation for which 7 1 1 3x and 7 x 3x T a Find 7 3 and 7 8 T 9 b a a

and v is orthogonal to w projwv 2i 6j Simplify your answer Use integers or fractions for any numbers in the expression Type your answer in terms of i and j V

Given vectors a 3 5 and b 0 6 find 5a 3b Write your answer in component form 5a 3b 0

Find the Fourier series off on the given interval 8 x 0 0 x 8 f x f x x 0 1 Give the number to which the Fourier series converges at a point of discontinuity of f If f is continuous on the given interval enter

Find f x and simplity f x A Which of the following shows the correct application of the quotient rule B OC X O D x 35 x 1 x 35 1 x 35 x 35 1 x 1 x 35 x 1 x 35 1 x 35 1 x 1 x

Let v be the vector from initial point P to terminal point P2 Write v in terms of i and j P 3 2 P 6 1

If a hypothesis is rejected at 95 confidence it O will sometimes be rejected at 90 confidence O will always be accepted at 90 confidence O None of these alternatives is correct will always be rejected at 90 confidence

Find the equation of the graph below Your answer should be in the form y Acos Bx C D Note A D may be negative 17 st 11 m 57 8 klo 6 7m 13 8 19 T

A graph G has 9 vertices all of degree 4 How many edges does G have Answer A graph G has 6 vertices all of degree k Also G has 12 edges What is k Answer A graph G3 has v vertices all of degree 4 Also G3 has 10 edges What is v Answer

Question 4 7 3 7 BE Deluxe coffee is to be mixed with regular coffee to make at least 46 pounds of a blended coffee The mixture must contain at least 9 pounds of deluxe coffee Deluxe coffee costs 5 per pound and regular coffee 3 per pound How many pounds of each kind of coffee should be used to minimize costs points O Points 0 of 1 Save To attain the minimum cost use pounds of deluxe coffee and pounds of regular coffee

you have saved 1500 for a down payment and the dealer has already included any applicable fees including taxes in the advertised price You plan on taking 5 years to pay off the loan The table below shows the price and interest rate for each option Price Interest Rate 17 945 15 000 2020 Honda Fit LX 2018 Honda Fit LX For both the new and the pre owned Honda Fit LX options do the following 1 Compute the amount to be financed considering that you have saved 1500 for a down payment 1 9 6 9 2 Use the formula for a regular payment on a fixed installment loan to determine the monthly payment Round your answer to the nearest dollar 3 Determine the total amount paid when repaying the car loan 4 Determine the finance charge for each purchasing option This is the difference between the total amount paid on the loan and the amount financed 5 Complete the following table Price Interest Rate Down Payment Amount Financed Monthly Payment Total Amount Paid 2020 Honda Fit LX 17 945 1 9 2018 Honda Fit LX 15 000 6 9

39 8 of consumers believe that cash will be obsolete in the next 20 years Assume that 7 consumer are randomly selected Find the probability that fewer than 3 of the selected consumers believe that c will be obsolete in the next 20 years The probability is Round to three decimal places as needed

65 DETAILS Sketch the graph of the equation 5x2 5y2 24x 40y 86 y 10 8 8 10 TOX

Problem 1 Simplify the following expressions using complex numbers Please write your answer in the form of a bi a 9 2i 8 5i b 32i 462

A cylinder has a diameter of 2 units and a height of 4 units find the volume and surface area of each Round your answer to the nearest tenth first decimal place Volume Surfar

A cylinder has a diameter of 9 units and a height of units 6 5 find the volume and surface area of each Round your answer to the nearest tenth first decimal place Volume Surface area

The area of a sector is 25 7 units squared The radius is 7 What is the central angle measure in degrees O 60 O 180 O45 90

A car tire is spinning a complete revolution every 0 60 seconds The valve stem is 2 Inches above ground at its lowest point and 26 inches at It s highest Describe the height of the valve stem as a function of time seconds if it begins at the bottom 26 in O 2 in Oh 14 sin 0 45 12 Oh 12 san 1 045 14 Oh 14 sun 0 15 12 h 12 sin 0 15 14

19 Using the substitution method the solution to the linear system x 2y 3 and y x 4 is a 1 3 b 5 1 c 1 1 d 11 4 20 Using the elimination method the solution to the linear system 4x 3y 9 and 4r 9y 21 is a 2 2 b 3 1 21 What is the product 8x 101 9x 11 72r 178r 110 b 72x 178x110 c 3 2 d 1 3 72x 2r 110 d 72x 2x 110

14 If ZB 72 c 15 cm and b 14 27 cm what is the measure of ZC to the nearest tenth of a degree A B 12 3 b 88 6 0 b C 90 0 d 99 9

Find an equation for the graph sketched below 5 4 3 1 f x 8 001165 IN 2 6 I 1 2 3 4 5 D

Find the median for the following list of numbers 104 117 127 137 143 174 The median is Type an integer or a decimal

Example 1 The population of a country on January 1 2011 was 6 7 million and the population on January 1 2017 was 11 9 million a Write an exponential model to represent the population of this country Lett be the numbers of years after 2011

What type of information does solving equivalent equations give u All of these answers are correct When the cost will be the same from two different companies selling the same products for different amounts The point at which to equations are equal and the variable has the same value Break even points Next

your score and answers at the end Complete this quiz to finish the assignment for ALG 2 Period 4 due on Apr 26 2023 question 1 of 5 Subtract x 3x 4 7x 5x 2 6x 8x 2 O 6x 8x 2 O 6x 8x 2

1 Let an be a convergent sequence of non negative real numbers Let a This question will go through a proof that a limx an a Prove that a 0 b If a 0 prove an 0 Hint an e is equivalent to an c If a 0 prove an a Hint Use the difference of squares formula an a an a a a limn x an

Determine the work done by a person lifting a 250 newton bag of sugar 2 meters Work newton meters

Recall that a 5 bit string is a bit strings of length 5 and a bit string of weight 3 say is one with exactly three 1 s How many 5 bit strings are there How many 5 bit strings have weight 0 How many 5 bit strings have weight 1 How many 5 bit strings have weight 2 How many 5 bit strings have weight 4 How many 5 bit strings have weight 5 How many 5 bit strings have weight 11

Graph the linear function using the slope and y intercept 4 y 5x 5 RE Use the graphing tool to graph the linear equation Use the slope and the y intercept when drawing the line Cligmto enlarge graph HE

Ex Convert the following relations from vertex to standard form a y 5 x 4 16 b y 3 x 2 y 3 x y 3 1 y 3

An initial sample of 246 g of a radioactive substance decays according to the function A t 246e 0 013t where t is given in years a How many grams of the substance will remain after 72 years Round your answer to one decimal place b What is the half life of the substance Round your answer to one decimal place

2 Suppose that X Unif 0 c for some constant c 0 Show that the random variable Y c X has the same cumulative distribution function as X and hence also the same density function Hence if X is uniformly distributed on 0 c so is c X 2

Current Attempt in Progress Pleasant Company has decided to begin accumulating a fund for plant expansion The company deposited 80 000 in a fund on January 2 2018 Pleasant will also deposit 40 000 annually at the end of each year starting in 2018 The fund pays interest at 4 compounded annually Click here to view the factor table What is the balance of the fund at the end of 2022 after the 2022 deposit For calculation purposes use 5 decimal places as displayed in the factor table provided Round answer to 2 decimal places eg 52 75 Fund balance

Current Attempt In Progress Sunland Company has a materials price standard of 2 00 per pound 6300 pounds of materials were purchased at 2 20 a pound The actual quantity of materials used was 6300 pounds although the standard quantity allowed for the output was 6000 pounds Sunland Company s materials price varlance is O 1200 U O 1260 F O 1260 U 60 U

DETAILS Consider the following 10 u 7 0 v 5 7 a Find u v U VE b Find the angle between u and v to the nearest degree 10

A ping pong ball is drawn at random from an urn consisting of balls numbered 2 through 10 A player wins 1 dollar if the number on the ball is odd and loses 1 dollar if the number is even What is the expected value of his winnings Express your answer in fraction form A card is drawn at random from a standard deck of playing cards no jokers If it is red the player wins 1 dollar if it is black the player loses 2 dollars Find the expected value of the game Express your answer in fraction form

Write each set in the indicated form If you need to use to indicate a pattern make sure to list at least four elements of the set As you answer below remember that the natural numbers are just the counting numbers This means that 0 is not a natural num and negative numbers are not natural numbers either a Descriptive form The set of positive multiples of 5 that are greater than or equal to 10 and less than or equal to 20 Roster form b Roster form 1 2 3 4 Descriptive form Choose one The set of natural numbers greater than or equal to 2 and less than or equal to 4 The set of natural numbers The set of odd natural numbers less than or equal to 3 The set of positive multiples of 3 that are greater than or equal to 6 0 0

BASIL Millions of pounds 48 42 36 PPF 30 24 18 12 6 0 0 6 Yosemite 12 18 24 30 36 CORN Millions of pounds 42 48 BASIL Millions of pounds 48 42 36 30 24 18 12 6 0 PPF BRO 6 I 1 Congaree A 12 18 24 30 36 CORN Millions of pounds 42 48 Yosemite has a comparative advantage in the production of while Congaree has a comparative advantage in the production of Suppose that Yosemite and Congaree specialize in the production of the goods in which each has a comparative advantage After specialization the two countries can produce a total of corn million pounds of basil and million pounds of Suppose that Yosemite and Congaree agree to trade Each country focuses its resources on producing only the good in which it has a comparative advantage The countries decide to exchange 6 million pounds of corn for 6 million pounds of basil This ratio of goods is known as the price of

Suppose a math class contains 25 students 12 females six of whom speak French and 13 males five of whom speak French Compute the probability that a randomly selected student speaks French given that the student is female

Use the ALEKS calculator to evaluate each expression Give your answers in radians Round them to the nearest hundredth If applicable click on Undefined cos 1 22 sin 0 97 tan 0 8 Undefined X

Decide whether the following statement makes sense or is clearly true or does not make sense or is clearly false Explain your reasoning The circular pattern in the floor is attractive because it exhibits the golden ratio Choose the correct answer below OA The statement does not make sense because circles are not naturally attractive figures in nature B The statement does not make sense because the golden ratio applies to rectangles and line segments not circles OC The statement makes sense because the golden ratio is equivalent to the ratio of the circumference to the diameter of a circle OD The statement makes sense because the golden ratio is equivalent to the ratio of the area to the circumference of a circle