Matrices & Determinants Questions and Answers

Suppose A is an invertible matrix with A LU where L is lower triangular and U is upper triangular In terms of L U please find L and U such that A U L U is upper triangular L is lower triangular

Find the LU factorization of A Ly To solve the system 1 2 47 3 3 2 1 8 22 using the LU factorization you would first solve and then solve Ux 10 x 33 18 2 41 3 10 Find the solution x 3 2 1

Consider the following vector equation 1 1 2 002 3 6 3 12 23 2 24 3 5 25 3 6 3 12 1 Explain how to find a simpler linear system that has the same solution set 2 Explain how to describe this solution set using set notation 7 17 8 19

avail We have to drink dirty water The colour and smell of the water shows that it needs has not been cleaned for two mo cleaning It is requested to look into the matter and do the needful With best regards Yours obediently Kunal Kalara Class XI C The Principal Govt Senior Secondary School Sardarshahar babara bject Con 9 Non availability of Towel and Soap at Washbasin You are student of Gout Senior Secondary School Sardarshahar There are no towels and ons at the washbasine of the toilets Write a letter to the principal of your school to make the proper arrangement of towels and soaps Ans Near Post Office Sardarshahar 18 December 20 Subject For non availability of towels and soaps at the washbasins of the toilets Sir 40 Spectfulls Midday me ater in th Thursd at burnt a Students requested With best Yours fai Aradhya Presiden Student Respectfully I want to bring into your kind attention to the problem of non availability of soups and towels for washing and wiping hands at the washbasins of toilets There are no soaps at the washbasins outside the toilets Sometimes there are towels but they are dirty and stinking It is very difficult for the students to wash hands properly and then wipe on such a dirty towel It is requested to look into the matter and make the arrangement of clean towels and soaps as early as possible 11 A L You are sit in t Fort F Bundi 15 No

na poll students were asked to choose which of six colors was their favorite The circle graph shows how the students answered If 6000 students participate the poll how many chose Purple Green 7 Red 10 Blue 13 Orange 21 Pink 10 Purple 39 00 X

7 Graph the inequality Label at least two points and Lesson 1 07 6x 2y 8 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 LO 6 8 10

Suppose that the lengths of human pregnancies are normally distributed with a mean of 266 days and a standard deviation of 17 days Complete the following statements a Approximately 95 of pregnancies have lengths between days and days b Approximately 283 days of pregnancies have lengths between 249 days and

Let G be the set of 2 x 2 matrices with integer coefficients in the range 0 hrough 7 odd integer determinants and binary operation given by ordinary multiplication followed by reduction of each entry mod 8 Your task is to rove that G is a group Follow these four steps a Prove closure is satisfied b Prove associativity is satisfied c Prove that there is an identity element d Prove that each element has an inverse

Either use an appropriate theorem to show that given set W is a vector space or find a specific example to contrary a b 8 b a b c 2 b 2d 5 d b 3d d b d are real

9 Three questions are asked to some US households when the U S Bureau of Labor Statistics BLS conducts a nationwide random survey to determine who is employed and who is not employed Based on information below what is the unemployment rate What about the labor force participation rate Questions Yes 1 Are you under 16 or institutionalized 10 million 2 Are you currently working 40 million 3 Have you been actively seeking work in the past four 8 million weeks No 50 million 10 million 2 million

Solve the equation Check your solution 2a 9 a 2 10 3

if dilating a shape maps it onto another shape then the two shapes are similar In this activity you will use dilation to determine whether the shapes in these graphs are similar Graph 1 Question 1 3 5 D 7 Hi A 3 Graph 2 III a

Which of the following graphs are functions Select all t apply A B 64444 12345 5482 11145 C D E F

oblem 7 Use Gaussian elimination to find a row echelon form not reduced row echelon form of the augmented matri for the following system and then use it to determine for which value of a the following system has infinitel many solutions x 2y 3z 1 x 2y 7 2x 3y az 0

63 Cost of Private College Education The table lists average annual cost in dollars of tuition and fees at private four year colleges for selected years Year 2013 2014 2015 2016 2017 Data from National Center for Education Statistics Cost in dollars 24 523 25 707 26 739 27 942 29 478 a Determine a linear function f x ax b that models the data where x 0 represents 2013 x 1 represents 2014 and so on Use the points 0 24 523 and 4 29 478 to graph f and a scatter diagram of the data on the same coordinate axes What does the slope of the graph indicate b Use the function from part a to approximate average tuition and fees to the nearest dollar in 2016 Compare the approximation to the actual figure given in the table 27 942 c A graphing calculator is required Use the linear regression feature of a graphing calculator to find the equation of the line of best fit

D for the matrix A 01 4 1 is No Decomposition possible NO Find pumutation matrix P such tha PA LU for come lower I upper triangular makine 13 3 PAZLU mu

Exercise 4 4 1 For each set of vectors use the most efficient method to determine if it is linearly independent or not 0 2 1 U i S ii S v1 iii S3 2 2 1 2 22 W 1 1 1 Uz V3 0 G W4 5 100 101 2 1

Complete the table shown to the right for the population growth model for a certain country k 0 Round to four decimal places as needed Save 2007 Population millions Projected 2017 Population millions Projected Growth Rate k 40 2 51 8

The average velocity i y displacement between 1 sec to 2 sec is y 8 t 21 1 86 t2 21 8 5 58 2 42m Avarage velocity 3 42 2 42 ii y displacement between 1 sec to 1 5 sec y 8 t 1 51 1 86 t2 1 51 8 x 0 5 2 325 1 675m Avarage velocity 1 675 3 35

Which matrices are in row echelon form 1 0 11 i 0 1 3 Lo 0 11 iv 131 All 010 0100 N i iv and vi O iv v and vi O U v and vi ii 00 OHOO 0000 0100 0010 NOTO NDIO 10 1 HF vi 10 0010 00000310 21002 251 0 0 0 0 11

1 point If the linear system has infinitely many solutions then k and h 7x 7y 4z 3 3x 7y 6x 4 13a 7y hz k

Solve the given formula for the indicated variable Electricity RR for R 1 1 1 R

3 Consider the matrix in Matlab notation A 1 a a 1 where the value of a gets close to 1 i e a 0 9 0 99 0 999 etc Study how it maps the unit circle x y Ax

2 10 points Consider the linear system where a and are constants x 3y z a 2x By z 1 2x 3y 4z 3 Find conditions on a and or such that a The system has a unique solution b The system has no solution c The system has infinitely many solutions Show Transcribed Text Please only answer if confident with the answer Please show all the steps and give detailed accura solution to the question Ensure to verify the answers as well Question is worth 10 marks so pleas

R is a linear transformation and that BD by rotating B counter clockwise by 45 degrees and doubling its length Also suppose That T T Suppose that T R we can find the image of T a What is T b What is T 1 1 c Find a matrix M so that for every x

23 How much water should be added to 50 ml of 80 percent acid solution to dilute it to a 70 percent acid solution ml 24 How many ml of 40 percent acid should be added to pure acid to make 40 ml of 45 percent acid Write your answer as a decimal rounded to the nearest thousandth if necessa x ml 25 An investment firm invested 3000 into two accounts 2200 went to an 12 annual rate account The rest went to a 7 annual rate account The interest the first year amounted to YOU

20 The Drama Club receives 1259 25 by selling 341 tickets to the opening night of the musical If the full price of a ticket is 5 25 and discount tickets for students and seniors are 0 75 each how many full price tickets were sold 21 Given two circles J and K with radii 5 in and 8 in respectively the ratio of the areas is O O both of these choices are equi ont

22 Given two similar triangles AABC and ADEF if AB 11 and DE 16 and AC 15 then what is the length of side DF Round to the nearest tenth O 11 7 O 21 8 O 21 3 O 10 3 23 How many ml of 10 percent acid should be added to pure acid to make 50 ml of 35 percent acid Write your answer as a decimal rounded to the nearest thousandth if necessary ml

Use the distributive property to find the product 4x 5x 4 0 power

Write the English phrase as an algebraic expression Let x represent the number Eight less than a number The phrase written as an algebraic expression is N

The slope m and a point P on a line are given Use the information to find three additional points on the line m P 5 6 3 Determine three points on the line with slope O A 2 8 2 11 6 14 O B 8 2 11 2 14 6 O C 9 1 12 3 15 7 On 1 0 2 121 1 7 151 and passing through 5 6

1 Solve each equation 1 x 6 10 A 4 16 C 4 B 8 26 D 20 0

Simplify the following expression All variables are nonzero 6x6 14x5 6x x6 14x5 UTE with nositive ato Ugo intogors or fractions for any nu

Find an equation of the line L 10 8 61 40 Q

Simplify the following expression 4 C C

2 1522 customers at a major retailer were surveyed whether or not they made a purchase and were satisfied with the service they received The table below organizes the responses Satisfied with Service Not Satisfied with Service Total Made a Purchase Did Not Make a Purchase Total Answer 1 pt 130 715 845 Reasoning Explanation 1 pt 494 183 677 a 2 ts What is the probability that a shopper selected at random made a purchase given that they were not satisfied with the service Write your answer as a fraction 624 898 1522 b 1 pt What is the probability that a shopper selected at random made a purchase or was satisfied with the service they received Write your answer as a fraction

Given that g x 2x 3x 11 find each of the following a g 0 b g 1 c g 2 d g x e g 1 t a g 0 11 Simplify your answer b g 1 Simplify your answer

Find the midpoint of the segment with the given endpoints 6 10 and 6 5 The mic Type a each ca

Intial Month Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 24 Annually 1 500 00 1860 Balance 6 Quarterly 1 500 00 1590 16 85 4 2 Monthly 1 500 00 1786 551 1843 7 1530 1560 6 1591 8 1623 6 1656 1 P

a Solve the following system of linear equation using Gauss elimination method Y 2z 2 I X 2y 2x ay 2 52 2 b b Find the condition on a and b such that the system has infinitely many solution c If b 4 Is the system of linear equation non homogeneous Give a reason

Find the product 4x 4 4x 4 16x 16 4x 4 4x 4 16x 16 Simplify your ans

Multiply 8k 5 9k 1 8k 5 9k 1 Simplify your an

Multiply the monomials 4x y6 8x y

Simplify the expression 3p q4 6 6 3p q4 Simplify your answer Use integers or fractions for any numbers in the or

Multiply the monomials 6a 9a6 6a 9a6

Simplify using the product rule y y6

Simplify the expression p p p 3 3 p p p Simplify your answer

Rationalize the denominator 11 N

3 Let A 6 1 3 1 and u 3 C 5 15 B3 c 23 a Compute Au and Ac if possible If not possible explain why not b Does the matrix equation Ar c have a solution c Does the matrix equation Ar b have a solution for any choice of b R d Restate the above question as a computationally equivalent question as done in page 2 of the notes

What is the equation of the graph that represents the parent function f x x stretched vertically by a factor of 2 and then shifted up 3 spaces A g x 2 x 3 OB g x 2x 3 C g x 2x 3 OD g x 2 x 3 4