Linear Algebra Questions and Answers

9 What is the general form of a quadratic function

5 Determine in which quadrants each of the following equation is an identity cos x cotx 1 cos x 1 cos x cos x a b

Write the augmented matrix of the system and use the matrix method to solve the system Write the augmented matrix of the system 1 260 1 20 0 3 5 740 2 1 1 260 2 GCIT Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA This system has exactly one solution The solution is Type an exact answer in simplified form OB This system has infinitely many solutions of the form z where z is any real number Type expressions using z as the variable C This system has no solution x y x 2y 2x 3y 5 2xy

Lamer decides to bike home from work He starts his trip being 9 miles from home He bikes of a pace of 5 miles per hour TASK Write an equation that would match the scenario in slope intercept form Do not include spaces in your equation

1 Melanie earns 1 850 33 in salary semi monthly when she works a normal 40 hour work week Find her semi monthly gross earnings if she works 10 hours of overtime in one semi monthly pay period and is paid time and a half for those hours O 2 170 63 1 952 40 2 078 56

Perform the indicated operation where possible 34 OA 1 13 4 OB O C 4 9 3 4 13 9

Let A OA OB O C O D 13 25 4 16 1 11 4 28 4 44 4 16 7 26 4 7 7 11 04 1 6 and B Find 4A B

Solve the system of equations If the system is dependent express solutions in terms of the parameter z x y z 10 x y 4z 6 3x y z 18 OA 4 4 40 1 60 OB 4 2 4 OC 4 4 2

Which graph represents a fonction 1 24 JE 24 SH 122 T 24 SH 34 32 S 11 11 DE E N B 3 P

At the start of the millennium State A was the third most populous state in the country followed by State B Since that time State B has experienced faster growth The populationy n millions of the given state in year x is approximated by the following equations where x 0 corresponds to the year 2000 In what year did State B overtake State A in population To the nearest million what was the population of these states at that time State B By 3x 112 State A 12y x 224 The year State B overtook State A was

The sizes of two matrices A and B are given Find the sizes of the product AB and the product BA whenever these products exist A is 4x 1 and B is 1x4 Find the size of the product AB Select the correct choice below and if necessary fill in the answer boxes to complete your choices A The size of product AB is 4 x 4 OB The product AB does not exist Find the size of the product BA Select the correct choice below and if necessary fill in the answer boxes to complete your choice O A The size of product BA is B The product BA does not exist

Find the following matrix product if it exists 2 O A 2 1 8 6 Select the correct choice below and if necessary fill in the answer box to complete your cho 2 1 8 2 6 Simplify your answer OB The product does not exist

The population y in the year x of the counties listed is approximated by the given equations where x 10 corresponds to 2010 and y is in thousands Solve this system of equations and interpre answer County A County B County C x 20y 108 x 10y 48 y 6 Select the correct choice below and if necessary fill in the answer boxes to complete your choice The system has exactly one solution The solution is 12 6 Type integers or fractions B The system has infinitely many solutions of the form y where y is any real number Type integers or fractions OC The system has no solution What does the answer represent Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA Two counties had the same population of in the year OB All three counties had the same population of in the year OC There will be infinitely many times when the three counties will have the same population On There

Give the equation of the vertical asymptote s of the rational function X 8 x 1 x 4 g x O A x 1 x 4 OB x 8 OC x 1 x 4

Find the indicated intercept s of the graph of the function x 7x x 3x 6 x intercepts of f x OA 7 0 OB 7 0 OC 0 0 7 0 O D 0 0 7 0

The product exchange function for gasoline x and heating oil y in hundreds of gallons per day is shown below 170 000 120x y 170 2x Sketch the portion of the function in Quadrant I of the graph and then find the x intercept and y intercept in order to estimate the maximum quantities of each product that can be produce Sketch the graph of Quadrant I for the function Choose the correct graph below OA OB AY 1 200 1 200 2 000 Q What is the maximum quantity of heating oil that can be produced Round to the nearest whole number as needed What is the maximum quantity of gasoline that can be produced 0 Round to the nearest whole number as needed O C 2 000 2 000 B 200 10 000 Q

Let A 1 be an odd integer and let p P2 Pn be all the primes A Put n 8p1p2 Pn Let q be a prim such that q 1 mod n As q is a prime q has a primitive root Let r be the smallest positive primitive ro of q i Find the Legendre symbols 2 a and P

Let 1 1 3 4 B H A 1 1 b 1 1 3 a Find a vector x that satisfies AT Ax AT b b Find a vector x that minimizes Ax 2b c Find the projection of 2b onto C A d Find the projection of 2b onto N AT

10 points Let QE Rnxk have orthonormal columns Show that if y belongs to the column space of Q then zl Q ull

Select all linear transformations that are projections OA T a b c a b c a a c B T a b c a 2c b a c a 2c Oc T a b c c b a OD T a b c a b c

Supposed the annual interest rate is 3 5 compounded monthly What is the monthly periodic interest rate Answer in percent rounded to two decimal places

Fill in the table using this function rule y 5x 3 X 2 0 2 4 y 0 0 0 X S

Consider 5 tripling in value every six months What s the resulting amount after 4 years Round to the nearest dollar

5 Find the Laplace Transforms of the following signals i x t cos 5x 1 2 u t 2 ii x t e sin 2t

the steps in the correct order to show that 6 divides n whenever n is a nonnegative integer using mathematical STEP VE STEP 61 0 0 i e 610 so the basis step is true 61 1 1 i e 610 the basis step is true By the inductive hypothesis 31 kk Clearly 31 3k k 1 but 3k k 1 is also odd as one of k or k 1 is even therefore 6 3k k 1 as well k 1 k 1 k 3k 3k 1 k 1 K k 3k k 1 0 By the inductive hypothesis 6 K K Clearly 31 3k k 1 but 3k K 1 is also even as one of k or k 1 is even therefore 6 3k k 1 as well As the sum of two multiples of 6 is again divisible by 6 6 k 1 k 1 Suppose that 6 K K

ow many elements are in the union of four sets if each of the sets has 104 elements each pair of the sets shares 50 elements each ree of the sets share 25 elements and there are 5 elements in all four sets

6 On the diagram two sides are marked Mark the angle that is considered the included angle in relation to these two sides 7 On the diagram two angles are marked Mark the side that is considered the included side in relation to these two angles 8 Put an X in the table to indicate which combinations of three pairs of congruent parts guarantee two triangles congruent SSS AAA SAS Proves congruence Does not prove congruence

2 Given the following quadratic equation state the x and y intercepts solutions of the form x 0 and 0 y the vertex and then use this information to sketch the graph a y x 2x 3 b y x 2x c y x 4x 2

In a dataset of 7 607 men and women with HIV the relationship between CD4 and several explanatory variables was examined Coefficients Model Constant MALE RACE BLACK RACE OTHER Unstandardized Coefficients B Std Error 21 243 10 279 10 541 13 130 35 268 491 Standardized Coefficients Beta 15 168 207 8 474 8 127 4 501 4 351 003 121 120 051 052 322 227 2 133 89 318 106 705 158 756 lung cancer AGE 2 135 a Dependent Variable CD4 LAST The variables are coded as follows Male 1 Male 0 Female Race black 1 Black Race 0 Not Black Race Race Other 1 Other Race 0 Not Other Race Lung Cancer 1 Has Lung Cancer 0 Does not have lung cancer Select all of the statements that are true about the relationships of each variable on CD4 Sig 001 836 001 001 001 001 Males have higher CD4 values than Females Having lung cancer decreases CD4 values Lung cancer has the largest effect on CD4 values Being black or an other race increases CD4 values compared to those who are white

Solve the problem Round to the nearest dollar Suppose that at age 25 you decide to save for retirement by depositing 95 at the end of every month in an IRA tha pays 5 25 compounded monthly How much will you have from the IRA when you retire at age 65 Find the interes OA 154 798 109 198 OB 176 512 130 912 OC 1 007 756 740 397 160 1 007 756 740 351 560 OD 153 202 107 602

Sequences and Functions Question 10 In a geometric sequence the ratio of any term divided by the term before it is always the same De Select one a 64 16 4 1 What is the ratio in the geometric sequence shown above O 14 02 O 2 O 4

Sequences and Functions Question 7 Nalini rents a bike and receives hourly texts about how much her bill will be At the end of her trip these are all the amounts she was sent a Hour 1 15 Hour 2 20 Hour 3 25 What equation could represent the sequence Select one O C 5h O C 15h O C 15h 5 O C 5h 10

A sequence is defined by the recursive definition belov f 1 16 f n f n 1 12 for n 1 Which sequence is generated by this definition Select one 18 O 16 4 8 20 O 12 28 44 60 O 28 40 52 64 O 16 28 40 52

Jessica is riding a taxi and is being charged the same rate per mile traveled After 1 mile she owes 8 After 2 miles she owes 14 After 3 miles she owes 20 a Which function represents the amount she owes after riding n miles Select one O A n 6n 14 O A n 6n 2 O A n 6n 8 O A n 8n

a Polynomials Question 6 What is the degree of the polynomial function graphed below 5 4 3 2 1 Select one O4 O 3 5 4 3 2 1 TH T 2 3 345 5 1 2 3 4 5

D Problem 2 Given the nonlinear equation ln 1 cos x a Show that the given equation has a unique solution p in 0 8 1 0 b Use the bisection method to find an approximation pn to the solution p such th Pn p 10 2 c Find an upper bound for the relative error of approximation Pn

Find the compound amount for the deposit Round to the nearest cent 140 000 at 1 10 compounded quarterly for 5 years OA 174 241 32 OB 147 871 27 OC 147 904 52 OD 141 935 62

Convert 2 21 radians into degrees Convert 0 37 radians into degrees Convert 5 83 radians into degrees Convert 3 55 radians into degrees You may use decimal approximation but your answer must be accurate to at least 3 decim

Let S be the set consisting of all 10 digits and all upper and lowercase letters Let U be the set of all ordered strings consisting of exactly four elements from S Construct an injective hash function h U N with the smallest possible value of maxUh u Modify your hash function to give a simply uniform map h to the set 0 30 In other words if U is a probability space with P u P u for all u u in U then the random variable h U 0 30 should have a uniform distribution

Q3 10 pts Use logical equivalence laws to show that p V q r p r q r Write Law name at every step HINT use p q pVq

The prefix Giga is equal to O 1 00 X 10 to the ninth power 1 00 X 10 to the negative ninth power 1 00 X 10 to the sixth power 1 00 X 10 to the negative sixth power

Convert 4 32 to 432 10 3 4 32 10 6 4 32 10 3 m milli

Construct a 90 confidence interval for the sample mean based on the following data x 14 90 and 3 8 O 144 068 145 932 O 144 215 145 785 O 144 341 145 659 O 144 599 145 401

Esp Chau borrowed 8000 at a rate of 19 compounded quarterly Assuming he makes no payments how much will F owe after 5 years Do not round any intermediate computations and round your answer to the nearest cent sm

Write an equation of the line below 7 6 5 4 3 74 6 2 5 6 6 7 8 0

One version of the Folium of Descartes is given by x y 4 9xy for what value s of x is the slope of the tangent line vertical O a 0 2041y b 0 2041y O c There is no place where the Folium has a vertical tangent O d 4 9000y 2 e 0 2041y 2 O f 0 6122y 2

14 points Find ker T range 7 dim ker 7 and dim range 7 of the following line ansformation 2 T R4 R defined by T x Ax where A A 1 L1 4 6 81 3 0 5 1 6 31

Demonstrate why for any whole number a b it is not possible for 2 b 2 a 2 Give answer about divisible by 2 even odd number of times As that s how the teacher wants it

15 For which of the following linear transformations is Null T 4 A T R R8 Range T 2 B T P3 P3 Range T 3 C T M2x3 M3x3 Range T 6 D T R5 R Range T 1

7 Let V R2 and define addition and scalar multiplication as follows u v u U v V U v 0 ku k u U ku 0 Which of the following vector space axioms does not hold A k u v ku kv B lu u C Closure under scalar multiplication D None of the above