Linear Algebra Questions and Answers

Describe each operation performed on the matrix b Obtain the reduced row echelon form of the augmented matrix you obtained in a augmented matrix 2 1 2 8 37 2 9 5 3 2 3 15 9

What is the solution to the equation 8 3 x 8 64 x 64

Determine the largest interval a b for which there is guaranteed to be a unique solution to the initial value problem below xy 9y exy x 6 y 5 1 y 5 0 y 5 2 The standard form for this equation is Simplify your answer Do not factor Type an equation

True or False Type T for the true entry and F for the false entry 1 The sum of two irrational numbers is irrational 2 The product of two irrational numbers is rational 3 Square of any integer is even 4 The product of two odd integers is odd 5 The sum of two odd integers is even

5 1 point Consider the graph of the quadratic function 50 What are the zeros of the function 4 0 and 1 4 and 1 only 5 and 0 only 5 4 and 1 10 10 10 x

A function h x with degree 3 has unique solutions If 2 of the solutions are imaginary numbers which statement is true The function h x must have 2 additional imaginary solutions The function h x must have 1 additional imaginary solution The function h x must have 1 additional real solution The function h x must have 2 additional real solutions

a 5pt Solve for x and simplify the answer 2x 6x 3 0 b 5pt Given the following quadratic equation state the x and y intereepts solutions of the form x 0 and 0 y the vertex and then use this information to sketch the graph y x 6x 5

a 5pt Evaluate the logarithm without using a calculator log 49 3 7 p 5pt Solve for x and round the answer to the nearest tenth 10 323

5 10pt Solve the system of equations 2x y 4 2 x 3y 5

In an evening statistics class 22 42 Part 1 of 3 Part 2 of 3 a What is the percentile rank of 30 26 28 An age of 30 is equivalent to the 40 Part 2 3 29 33 Part 3 of 3 31 40 The age of 38 30 b What is the rank from the top of 30 An age of 30 has a rank of 12 in this data set th st nd rd 19 32 percentile c What age corresponds to the 50th percentile corresponds to the 50th percentile 20 24 43 44 34 35 39 23

Work performed by one person for others such as repair work tutoring hair styling ha mprovements etc are called O labor O goods O services

A mapping 7 R R2 is expressed by the transformation matrix below 2 51 A 35 3 71 a State the condition for an orthogonal transformation Is T an orthogonal transformation Give your reason 4 marks b Find the image of the given vector below using the transformation matrix A 5 u 1 mark

1 X X 1 Calculate a Spectral decomposition of the matrix b Rank 1 approximation of the matrix

In Exercises 7 9 use the diagram ST 12 to find the given length 7 CU 8 UR 9 the radius of C Q 7x10 C R 3x 6 V T

Find the value of x Assuming all variables are integers X 1 y 2 Z 3 x float x y 2 3 A 4 5 B No answer C 5 5 D 4 E 5

3 5pts Rewrite the integral 1 1 1 y SSS f x y z dz dy dx as an 0 equivalent iterated integral in the five other orders 2 1 y 1

Uncertainties and complexities can always be avoided in HIT implementation True False

A healthcare administrator assigned in a HIT project implementation must focus only on timely implementation of the project True False

with 90 sides with 176 4 as interior angle with 76 sides with 14 760 as sum of interior angles 1 A polygon 2 A polygon 3 A polygon 4 A polygon 5 A polygon with 69 sides 6 A polygon with 175 5 as interior angle 7 A regular polygon with 20 sides 8 A regular polygon with 57 sides 9 A polygon with 179 964 as interior angle 10 A polygon with 10100 sides

Let G be a connected graph with n vertices where n 3 Prove that if each vertex of G has degree at least n 1 2 then G contains a Hamiltonian cycle

Let s define a matrix A A a b c d 1 If det A ad bc 5 find the value of a when b 2 c 3 and d 4 2 Consider a second matrix B 2 3 1 1 Compute the product of AB

Find the general solution of the system x t Ax t for the given matrix A A 5 21 11 4 11

Find all solutions of the equation z 3x 6 0 by using the quadratic formula Express the solutions in the form a bi Use sqrt if needed for constant First input the solution with b 0 here the real number a equals and the real number b equals Then input the solution with b 0 here the real number a equals and the real number b equals

For a certain company the cost for producing items is 35x 300 and the revenue for selling z items is 75x 0 5z2 The profit that the company makes is how much it takes in revenue minus how much it spends cost In economic models one typically assumes that a company wants to maximize its profit or at least wants to make a profit Part a Set up an expression for the profit from producinand selling z items We assume that the company sells all of the items that it produces Hint it is a quadratic polynomial Part b Find two values of that will create a profit of 50 The field below accepts a list of numbers or formulas separated by semicolons e g 2 4 6 or z 1 z 1 The order of the list does not matter To enter Va type sqrt a H Part e Is it possible for the company to make a profit of 2 500

2 points a Make an example of a quadratic function in vertex form b What is the equation of axis of symmetry of your function

State restrictions and simplify a b 2 x 2x 1 x 1 x 1 x x 1 x 2x 3 r 3x 2 x x 2

Dhana is able to prove the following about functions fand g What has she shown about these two functions The two functions are reflections of each other The composition of the two functions is commutative The product of the two functions is always x The two functions are inverses of each other f g x g f x x

What is the value of x in 3 42 1 24 Round your answer to the nearest tenth Answer tyno ve

Which expression is equivalent to A B C D 3x 6x 4 3x 3x 2 X X 2 12 2x 3x 2 2 Show explain how you would add these expressions 3 Which answer choice would be best X 3x 2 1 This question comes from adding subtracting rational functions Adding and subtracting rational functions means that the denominators must be the

Which statement is true The binomial x 5 is not a factor of the polynomial x 7x 13x 15 because wh x 7x 13x 15 is divided by x 5 the remainder is 0 O The binomial x 5 is a factor of the polynomial x 7x 13x 15 because when x 7x 13x 15 is divided by x 5 the remainder is 0 32 The binomial x 5 is a factor of the polynomial x 7x 13x 15 because wh x 7x 13x 15 is divided by x 5 the remainder is not 0 The binomial x 5 is not a factor of the polynomial x 7x 13x 15 because when x 7x 13x 15 is divided by x 5 the remainder is not 0

A polynomial has factors x x 3 3x 2 and x 7 What are the zeros of the function the polynomial defines 0 3 2 3 7 3 2 3 7 3 2 3 7 0 3 2 3 7

500 400 300 200 100 TU 15 20 25 2019 StrongMind Created using GeoGebra 1 What linear equation in slope intercept form does this graph represent 2 What was your thought process Explain how you found your equation Use complete sentences in your response 3 a Write a real world situation that could be modeled by this linear equation Your real world example should be different other posts b Explain how you labeled the z axis and y axis based on the situation you wrote in 3a

State restrictions and simplity a b 3xy 3y 3x y 12y 3x 5x 2 x 2x 1

15 Suppose that is an acute ang such that tan 0 3 Find sin 0 O O 3 4 1 10 O 1 4 O O 7 10 3 10

19 Solve for a when 3 5 O O O O O X X In X In 3 In 5 x 5 In 5 In 3 x ln 5 3 3 5

A parabola can be drawn given a focus of 6 1 and a directrix of x 2 Write the equation of the parabola in any form 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 y 9 10 11 12 directrix 1 3 4 5 6F 6 1 9 10 11 12 X

Name 1 APPLICATION Investment Growth and Exponential Equations UNIT INTA You are given 10 000 that will triple every year for the next 5 years Write an equation that a represents this situation where y represents the value of the investment after 5 years Level 1 2 Your equation has three numbers starting value growth factor and the exponent You are allowed to double one of these numbers Which one do you think will result in the highest outcome Explain your reasoning b Double the growth factor 3 Let s find out which one gives the highest outcome a Double the starting value c Double the exponent 4 Which double resulted in the highest return on your investment 5 Think about the change that resulted in the highest return on your investment What does that represent in the real world context of the original situation After performing this activity if you had to give advice to someone making an investment that results in exponential growth what would you tell them

A couple wants to invest up to 20000 They can purchase a type A bond yielding 11 75 return and a type B bond yielding a 12 75 return on the amount invested They also want to invest at least as much in the type A bond as in the type B bond They will also invest at least 10000 in type A and no more than 15000 in type B bond How much should they invest in each type of bond to maximize their return Let x be the amount invested in type A bond and y the amount invested in type B bond a Write the objective function to be maximized P b The feasible region has 3 corner points List the three points Corner points c Determine the amount to be invested in each bond to maximize the return and determine the maximum return Amount to be invested in type A bonds Amount to be invested in type B bonds

Given the following equation y 3 x 5 x 9 x 5 x 9 are O the x intercepts O the y intercepts Next O not the x intercepts O the square values ALA Repo quest

Connie keeps her sports card collection in a 54 page book Each page has 9 slots for cards Football cards take up the first 18 pages of the book Use the drop down menus to describe how many slots in the book may be filled with baseball cards Click the arrows to choose an answer from each menu The inequality Choose may be filled with baseball cards A graph of this inequality would have Choose can be used to represent the number of slots in the book that Choose and be shaded to the

2 Use the square root property to solve the equation x 8 2 Select one A 2 3 B 2 8 2 8 C 8 2 D 8 2 Show Transcribed Text x 4 7 3 Use the square root property to solve the equation Select one A 2 7 c

1 Find the radius of a circle which has a sector of area 15 square miles determined by a central angle radian 7 miles Type an integer or decimal rounded to three decimal places as needed

Consider the following X C in R a Find the coordinate vectors x and x c of x with respect to the bases B and C respectiv b Find the change of basis matrix P C B from B to C

Orthogonally diagonalize the matrix 8 A 1 2 3 2 on orthogonal matrix and diagonal matrix D such that QT AQ D

A 3 4 5 6 7 B 3 6 2 5 7 Select all that apply A A B B ACB C BCA D ACB E BCA

tement is true or false If it is false give the reas E book TV radio Choose the correct answer below OA The statement is true is an element of the set OB The statement is true is a subset of the set OC The statement is false is a not a subset of the set OD The statement is false is a set not an element

Perform the indicated calculation 5 2 5 5 in Z6

Determine whether T is a linear transformation T P P defined by T a bx cx2 a b x 7 b x 7

Use the given function to complete parts a through e below f x 3 x 1 x 9 a Use the Leading Coefficient Test to determine the graph s end behavior The graph of f x falls left and rises right O The graph of f x rises left and falls right The graph of f x rises left and rises right The graph of f x falls left and falls right b Find the x intercepts The x intercept s is are Type an integer or a decimal Use a comma to separate answers as needed At which zero s does the graph of the function cross the x axis Select the correct choice be O A The graph crosses the x axis at the zero s Type an integer or a decimal Use a comma to separate answers as needed B There are no zeros at which the graph crosses the x axis At which zero s does the graph of the function touch the x axis and turn around Select th OA The graph touches the x axis and turns around at the zero s ma to separate answers as needed

Solve for x p CORNE PLA D 14 03 10 H O te VE 55 E 60 L F G 5x 15