Q: If a 3 × 8 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT.
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Q: a) If a 7 × 5 Matrix A has rank 2, find dim(Null A), dim (Row A) and rank AT
A: 1) Given 7×5 matrix rank(A)=2 using rank nullity theorem we have rank A + null A= number of…
Q: Suppose that A is a 18 x 7 matrix and the null space of A has dimension 3. What is the rank of A?
A: For a m×n matrix, the number of rows is equal to m and the number of column is equal to n .
Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).
A: Singular matrix mean its Determinant is equal to 'zero' .
Q: Verify that if r < s, then rows rand s of a matrix can be interchanged by performing 2(s - r) - 1…
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Q: Find a matrix A such that e [-] -2 is a solution for Ax= x'.
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Q: The output matrix is X: (Round HooimaL
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Q: Find a 2 x 1 matrix x with entries not all zero such that 2 Ax = 3x, where A = 1 2
A: Given matrix is A=2 11 2 and condition is Ax=3x
Q: Find the greatest value of A that make the matrix 2 – A 2 A singular. -6 5 – A
A: Eigenvalues and determinants
Q: If a 6 x3 matrix A has rank 3, find nullity A, rank A, and rank AT. nullity A = rank A= rank AT=
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Q: 2) An n x n matrix A is called nilpotent if Ak = 0 for some positive integer k. Show that if A + 0…
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Q: a) Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.
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Q: Find a 3 × 1 matrix x with entries not all zero such that
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Q: If the null space of an 8 × 5 matrix A is 2-dimensional, what is the dimension of the row space of…
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Q: Find ∣A−1∣ for the matrix
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Q: Find an example of a singular 2 × 2 matrix satisfying A2 = A.
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Q: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…
A: Multiple : Let A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…
Q: Find a 3 x 1 matrix x with entries not all zero such that 1 2 -1 Ax = 1x, where A 1 1 -4
A: A=1 2-11 0 14-4 5 Now let x=abc be the required matrix. Now consider, Ax=1x⇒1 2-11 0 14-4…
Q: Find the size of the matrix 0.
A: Count the number of rows and columns
Q: (2) Let A = UDV" be a SVD of a square matrix A. What is the sum of squares of the singular values,…
A: We find the sum of squares of the singular values in terms of A.
Q: Suppose A is a 4 × 4 coefficient matrix If possible, find the entries of a matrix T that perform the…
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Q: • Is it possible for a 5 x 5 matrix to be invertible when its columns do not span R°? Why or why…
A: According to the Invertible matrix theorem, the matrix with n x n order cannot be invertible if its…
Q: A transversal of an n × n matrix is a collection of n entries where no two are in the same row and…
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Q: What is trace of matrix (2A+3B)
A: Find the trace of the matrix(2A+3B)
Q: [3 Compute the mnatrix exponential et for the diagonal matrix A = %3D
A: We have to find the exponential matrix of given diagonal matrix
Q: Compute the indicated power of the matrix.
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Q: What does it mean to say that A is a matrix with dimensionm n?
A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…
Q: Can the null space of a 3 × 6 matrix have dimension 2? Explain.
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Q: A nxn matrix is called nilpotent if there exists an integer p such that AP=On. Show that each of the…
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Q: If the null space of a 9x5 matrix A is 2-dimensional, what is the dimension of the row space of A?…
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Q: Suppose a 3x8 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…
A: Ans: Given a 3×8 matrix has a rank 3. We want to find the dimension of the null space, dimension of…
Q: Determine all the n × n− matrix A with the range such that A2 = A.
A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…
Q: If the null space of a 7 × 6 matrix is 5-dimensional, what is the dimension of the column space of…
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Q: 18. Let A be a 3 x 5 matrix with 2 pivots. What is the dimension of Nul(A)?
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Q: Suppose A is a 5x9 matrix and Rank(A) = 3. Find dim(null(A)). 1 O 2 Оз O 6
A: Solution of the given problem is as follows:
Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner
A: Now we will find A-1 . Where I is identity matrix.
Q: 8.) Find the LU-factorization of the following matrix 1 2 2 2 3. 1.
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Q: If the null space of a 7 x 6 matrix A is 5-dimensional, what is the dimension of the column space of…
A: We solve given problem with the help of rank nullity theorem
Q: Associated with every square matrix A is a real number denoted by |A| called the __________ of A .
A: |A| denotes the determinant of a matrix A. Hence,
Q: Suppose A = QR is a QR factorization of an m × n matrix A (with linearly independent columns).…
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Q: [2 3 find the invers of matrix A by using the elementary row operation, where A = 5.
A: For finding the inverse of any matrix A, at first we augment it with an identity matrix on the…
Q: Describe the range and null space of any n × n nonsingular matrixand the n × n zero matrix.
A: According to the given information first it is required to calculate the range of n×n non-singular…
Q: Find the greatest value of A that make the matrix 2 – 9 – A - A singular. – 6 -2 – X.
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Q: Suppose A is a 5x9 matrix and Rank(A) = 3. Find dim(null(A)-). O 1 3 O 6
A: Given; A is a 5*9 matrix and Rank(A)=3.
Q: 29 What numbera in A-L makes A-QA@ possible (where Qis an orthognael matrix and A is an Zero or 1??
A: We shall solve this question by just using the definition of an orthogonal matrix. We know that a…
Q: A matrix in which there is only one row and any number of columns is said to * .be matrix
A: Given: Expression is ^-*33*425 In the prefix form of an expression, a binary operator…
Q: If a 6 × 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT
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Q: a) In statistical theory, a common requirement is that a matrix be of full rank. That is, the rank…
A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…
Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.
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- Kentville, a community of 10,000 people, resides next to a krypton mine, and there is a concern that the emission from the krypton smelter have resulted in adverse effects. Specifically, Kryptonosis seems to have killed 12 of Kentville’s inhabitants last year. A neighboring community, Lanesburg, has 25,000 inhabitants and is far enough from the smelter to not be affected by the emission. In Lanesburg, only three people last year died of Kryptonosis. Given that the number of deaths in Kentville and their causes last year were: Heart attack=7 Accidents=4 Kryptonosis=12 Other=6 What is the risk of dying of Kryptonosis in Kentville relative to non-contaminated locality?What is the risk of dying of Kryptonosis in Kentville relative to deaths due to other causes? How many times the chance of dying of Kryptonosis compared to dying of accidents ? How many times the chance of dying of Kryptonosis compared to Other causes?A marketing research group conducting a telephone survey must contact at least 150 wives and 120 husbands. It costs P100 to make a daytime call and (because of higher labor costs) P150 to make an evening call. On average, daytime calls reach wives 30% of the time, husbands 10% of the time, and neither of these 60% of the time, whereas evening calls reach wives 30% of the time, husbands 30% of the time, and neither of these 40% of the time. Staffing considerations mean that daytime calls must be less than or equal to half of the total calls made. How many should be interviewed at each period to minimize the cost of completing the survey? fomulate the LP Model; identify the decision variables used in the model; and determine the optimal solution using graphical method.A survey was conducted of two types of marketers. The first type being marketers that focus primarily on attracting business (B2B), and the second type being marketers that primarily target consumers (B2C). It was reported that 518 (88%) of B2B and 246(59%) of B2C marketers commonly use a business social media tool. The study also revealed that 301(51%) of B2B marketers and 248(59%) of B2C marketers commonly use a video social media tool. Suppose the survey was based on 590 B2B marketers and 420 B2C marketers. Complete parts (a) through (c) below. At the 0.05 level of significance, is there evidence of a difference between B2B marketers and B2C marketers in the proportion that commonly use the business social media tool? Let population 1 correspond to B2B marketers and population 2 correspond to B2C marketers. Choose the correct null and alternative hypotheses below. A.H0:π1=π2 H1: π1≠π2 BH0:π1≥π2 H1:π1<π2 C.H0:π1≤π2 H1:π1>π2…
- A software organisation employs 80,000 staff members. 16,000 employees are inthe sales team, 24,000 are in the customer support team and 14,000 are in thesoftware development and HR departments. What percentage of theorganisation’s employees are a part of the finance team, if the size of the financeteam makes up two-fifths of the remainder?For a telephone survey, a marketing research group needs to contact at least 600 wives, 480 husbands, 400 single adult males, and 440 single adult females. It costs $3 to make a daytime call and (because of higher labor costs) $5 to make an evening call. The file P03_31.xlsx lists the results that can be expected. For example, 30% of all daytime calls are answered by a wife, 15% of all evening calls are answered by a single male, and 40% of all daytime calls are not answered at all. Due to limited staff, at most 40% of all phone calls can be evening calls. a. Determine how to minimize the cost of completing the survey. b. Use SolverTable to investigate changes in the unit cost of either type of call. Specifically, investigate changes in the cost of a daytime call, with the cost of an evening call fixed, to see when (if ever) only daytime calls or only evening calls will be made. Then repeat the analysis by changing the cost of an evening call and keeping the cost of a daytime call…Data from the Bureau of Labor Statistics indicates that in a certain month, 39.9% of the labor force had a high school diploma or fewer years of education, 29.6% had some college or an associate's degree, and 38.5% had a bachelor's degree or more education. Of those with a high school diploma or fewer years of education, 7.6% were unemployed of those with some college or an associate's degree, 3.2% were unemployed and those with a bachelor's degree or more education, 2.3% were unemployed find the probability that a randomly-chosen labor force participation have some college rent associates degree given that he or she is employed.
- In the Black Swan briefly explain Yevgenia’s Black Swan, and the concepts of Mediocristan and Extremistan. Provide examples of each.Globally, 35% of all ridged brittleshell tortoises have spots on their shells. A herpetologist in Citition collects a sample of 38 ridged brittlesell tortoises and finds that 16 of them have spots on their shells. The herpetologist would like to test the claim that the proportion of ridged brittleshell tortoises in Cititon with spots on their shells is greater than 35%. The herpetologist ends up rejecting the null hypothesis. If the actual proportion of ridged brittleshell tortoises in Cititon with spots on their shells is 41%, then what type of error, if any, has occurred? In the problem above, what is the test statistic?A electronics retailer list the sales (in thousands) of certain products in three cities for the prior quarter. During that period tablets sold for $241, laptops sold for $505, cell phones sold for $437, and DVR sold for $1,564. City 1 City 2 City 3 Tablets 44 57 39 Laptop Computers 64 77 68 Cell Phones 31 53 69 Personal DVR 30 76 54 City 1's total sales : City 2's total sales : City 3's total sales :
- A car agency has offices in Phoenix, Denver and Chicago. The agency allows one- or two-way rentals so that cars rented in one location may end up in another. Statistics show that at the end of each week 70% of all rentals are twoway. As for the one-way rentals: from Phoenix, 40% go to Denver, and the rest to Chicago; from Denver, 60% go to Chicago and the rest to Phoenix; from Chicago, 40% go to Denver and the rest to Phoenix; (a) Express the situation as s Markov chain. (b) If the agency starts the week with 100 cars in each location, what will the distribution be like in two weeks (two-step transition probability matrix)? (c) If each location is designed to handle a maximum of 120 cars, would there be a long run space availability problem in any of the location?A dietician prepares a diet specifying the amounts a patient should eat of four basic food groups: group I, meats; group II, fruits and vegetables; group III, breads and starches; group IV, milk products. Amounts are given in “exchanges” that represent 1 oz (meat), 1/2 cup (fruits and vegetables), 1 slice (bread), 8 oz (milk), or other suitable measurements. (a) The number of “exchanges” for breakfast for each of the four food groups, respectively, are 2, 1, 2, and 1; for lunch, 3, 2, 2, and 1; and for dinner, 4, 3, 2, and 1. Write a 3*4matrix using this information.(b) The amounts of fat, carbohydrates, and protein (in appro-priate units) per exchange in each food group, respectively, are as follows.Fat: 5, 0, 0, 10Carbohydrates: 0, 10, 15, 12Protein: 7, 1, 2, 8Use this information to write a 4*3 matrix.(c) There are 8 calories per exchange of fat, 4 calories per ex-change of carbohydrates, and 5 calories per exchange of protein. Summarize these data in a 3*1 matrix.A health researcher studying child birth is interested in the possible effect that smoking by the mother during pregnancy has on the baby's birth weight. To investigate, the researcher conducts an observational study by reviewing 400 records of women in their twenties who have recently given birth for the first time. For each record, he notes whether or not the woman smoked during pregnancy and the baby's birth weight, in addition to the woman's education level, and age. From the data, the researcher creates two groups: women in their twenties who smoked during pregnancy and women in their twenties who did not smoke during pregnancy. Then he compares the average birth weight between the two groups. (a)Why might the researcher have chosen to perform an observational study (by gathering information from past records) and not a randomized experiment (by assigning pregnant women to either the smoking or nonsmoking group at random)? Choose the best answer from the choices below. In a…