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Combinatorics: please do (a) and (b) 12 Suppose that two orthogonal 5 x 5 Latin squares both have 1 2 3 4 5 as the last row. (a) Is it possible for them to have the same 1, 3 entry? (b) What does...
combinatorics: parts a and b 5) (a) Determine whether or not the two Latin squares are orthogonal. Show your work 3 41 1 2 3 4 3 4 1 2 3 4 1 2 2 3 4 1 3] L4123 2 3 4 1 4 1 (b) How many 4x4 Latin s...
combinatorics: parts a and b
5) (a) Determine whether or not the two Latin squares are orthogonal. Show your work 3 41 1 2 3 4 3 4 1 2 3 4 1 2 2 3 4 1 3] L4123 2 3 4 1 4 1 (b) How many 4x4 Latin squares can be in a family of orthogonal order 4 Latin squares? Explain.
5) (a) Determine whether or not the two Latin squares are orthogonal. Show your work 3...
Problem 5. (20 pts) Let r,n N be two natural numbers with r < n. An...
Problem 5. (20 pts) Let r,n N be two natural numbers with r < n. An r x n matrix M consisting of r rows and n columns is said to be a Latin rectangle of size (r, n), if all the entries My belong to the set {1,2,3,..., n), for 1Si<T, 1Sj<T, and the same number does not appear twice in any row or in any column. By defini- tion, a Latin square is a Latin rectangle of size...
Problem 1 Suppose you have two dice to toss (both of them are fair). a) What...
Problem 1 Suppose you have two dice to toss (both of them are fair). a) What is the probability of that the total of the two dice will add up to 7 or 11? b) What is the probability of that the total of the two dice will add up to a number other that 2 and 12? Are the events E1 first die shows a 3 E2 total of two die is 6 Independent events? c) d) Given the...
About linear algebra,matrix; 2. (a) Use Octave as a Calculator to answer this question. Suppose that A and B are two 8 x 9 matrices. The (i.j)-entry of the matrix B is given by i *j -1. The (i. j)-en...
About linear algebra,matrix;
2. (a) Use Octave as a Calculator to answer this question. Suppose that A and B are two 8 x 9 matrices. The (i.j)-entry of the matrix B is given by i *j -1. The (i. j)-entry of the matrix A equals 0 if i + j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? ii. Is vector u 9,64,-71,...
3. Suppose you and your class mate have to do a group assignment. Both of you...
3. Suppose you and your class mate have to do a group assignment. Both of you can decide to work or shirk. If you both work, then both will get a good mark but both incur the cost of working. If one person works, you get a bad mark but the person who shirked will not have to put in the effort. If both shirk then the students fail. The following table represents the individuals’ utilities (as always the first...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. ...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. We want to know what is the minimum number of swaps that we need in order to get from number A to B, where in each swap we choose two digits of a number and simply swap them For simplicity, we assume that A and B do not have the digit 0 in them, and that A and B have the set...
I have partial answers for some of them, but not confident at all in them 2)...
I have partial answers for some of them, but not confident at
all in them
2) Consider two consumers, Tom and Robert, choosing between goods 1 and 2. Both have the same income of $60 (M=60) and the prices of goods 1 and 2 are P S10 and P = $7.5. Their initial budgets and indifference curves are below. Robert Tom Good 2 Good 2 P = 10 P2=13.3 NWU ON 1 2 3 4 5 6 7 8 9...
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e....
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
from part 5-12 plz dont do 1-4 BUNUS Assignment! A Sample Data AnalySIS III Licer Please...
from part 5-12 plz dont do 1-4
BUNUS Assignment! A Sample Data AnalySIS III Licer Please answer all of the following questions. Make sure you show all your work, providing snapshots from Excel as well as listing all formulas and relevant explanation, as needed. We are interested in exploring the relationship between the income of professors (measured in thousands of dollars) and the number of years they have been employed by the university. We collect the following data from eight...
I have attached the questions and the solutions. Please do all of questions 4 and 5 4.a) A matrix A is said to be o...
I have attached the questions and the solutions. Please do all
of questions 4 and 5
4.a) A matrix A is said to be orthogonalifA". Arv.equivalently,if AA"-A"Asl If A is anorthogonal matrix with integer entries show that every row of A has exactly one nonzero entry which is equal to ± 1. b) If A and B are invertible matrices of the same size show that adj AB adj B(adj A 5 a) Find all unit vectors parallel to the...
combinatorics: parts a and b
5) (a) Determine whether or not the two Latin squares are orthogonal. Show your work 3 41 1 2 3 4 3 4 1 2 3 4 1 2 2 3 4 1 3] L4123 2 3 4 1 4 1 (b) How many 4x4 Latin squares can be in a family of orthogonal order 4 Latin squares? Explain.
5) (a) Determine whether or not the two Latin squares are orthogonal. Show your work 3...
Problem 5. (20 pts) Let r,n N be two natural numbers with r < n. An r x n matrix M consisting of r rows and n columns is said to be a Latin rectangle of size (r, n), if all the entries My belong to the set {1,2,3,..., n), for 1Si<T, 1Sj<T, and the same number does not appear twice in any row or in any column. By defini- tion, a Latin square is a Latin rectangle of size...
Problem 1 Suppose you have two dice to toss (both of them are fair). a) What is the probability of that the total of the two dice will add up to 7 or 11? b) What is the probability of that the total of the two dice will add up to a number other that 2 and 12? Are the events E1 first die shows a 3 E2 total of two die is 6 Independent events? c) d) Given the...
About linear algebra,matrix;
2. (a) Use Octave as a Calculator to answer this question. Suppose that A and B are two 8 x 9 matrices. The (i.j)-entry of the matrix B is given by i *j -1. The (i. j)-entry of the matrix A equals 0 if i + j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? ii. Is vector u 9,64,-71,...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. We want to know what is the minimum number of swaps that we need in order to get from number A to B, where in each swap we choose two digits of a number and simply swap them For simplicity, we assume that A and B do not have the digit 0 in them, and that A and B have the set...
I have partial answers for some of them, but not confident at
all in them
2) Consider two consumers, Tom and Robert, choosing between goods 1 and 2. Both have the same income of $60 (M=60) and the prices of goods 1 and 2 are P S10 and P = $7.5. Their initial budgets and indifference curves are below. Robert Tom Good 2 Good 2 P = 10 P2=13.3 NWU ON 1 2 3 4 5 6 7 8 9...
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
from part 5-12 plz dont do 1-4
BUNUS Assignment! A Sample Data AnalySIS III Licer Please answer all of the following questions. Make sure you show all your work, providing snapshots from Excel as well as listing all formulas and relevant explanation, as needed. We are interested in exploring the relationship between the income of professors (measured in thousands of dollars) and the number of years they have been employed by the university. We collect the following data from eight...
I have attached the questions and the solutions. Please do all
of questions 4 and 5
4.a) A matrix A is said to be orthogonalifA". Arv.equivalently,if AA"-A"Asl If A is anorthogonal matrix with integer entries show that every row of A has exactly one nonzero entry which is equal to ± 1. b) If A and B are invertible matrices of the same size show that adj AB adj B(adj A 5 a) Find all unit vectors parallel to the...
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