Problems 61-70 refer to the following transition matrix
Find the probability of going from state
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- SECTION I: MATRIX OPERATIONS [2 -1 1.5 A = 2.75 1 -1 -3 -0.5 4 0.25 0.1 0.2 -15.2 0.6 D = 0.05 [sym. 7 2 -10 0 0.25 0 1 1 E = -15.575 1.975 2 1.4 -0.9 1.075 1.2 5.9 1. Find the TRANSPOSE of B. Name it, "Matrix F". 2. Find the PRODUCT of Matrices A and F. Name it, "Matrix G". 3. Matrix D is symmetric. Find the SUM of Matrices G and D. Name it, "Matrix H". 4. Find the DIFFERENCE between Matrices H and E. That is: [H] - [E]. Name it, "Matrix I". 5. AUGMENT Matrix C with Matrix I. Write them in both in MATRIX AND EQUATION FORM. Remember: Ax=B, or in this case, Ix=C. Use the variables: w, x, y and z when writing them in equation form. 6. Using the formula discussed in class, determine if Matrix is DIAGONALLY DOMINANT. If yes, proceed to section 2. If not, rearrange Matrix I so that it becomes diagonally dominant. Since we have previously augmented matrix I with C, rewrite the system of linear equations (just as with Item 5) with the CORRESPONDING rows from matrix C both in MATRIX AND…arrow_forwardGiven the input coefficient matrix for a hypothetical economy made up of only two industries as A =0.1 0. 3 0. 5 0.2. Provide an economic explanation for each of the elements in Aarrow_forward1. Given the input-coefficient matrix for a hypothetical [0.1 0.5] A = economy made up of only two (2) industries as provide an economic interpretation for each of the elements in matrix A. 0.3 0.2arrow_forward
- Question 3 The owner decides he wants to employ only new trainee staff. He also wants only new trainee staff who are siblings of his permanent staff. He believes that each month, 5% of his permanent staff would have a sibling who would be suitable to start as a trainee staff member. His staffing model would therefore be defined by the rule S, = 75, + FS,, and the matrix S, giving the number of staff at the end of the first month in January 2013 would therefore be defined as S-75, + FS, where 0 0 0 0 0 0 0.05 0 0 0 0 o 0 0 0 o 0 0 0 10 0.8 0 0 0 T = O 09 0.7 0 20 and F= 60 0.2 0.1 03 1 where the matrices T and 5, are the same matrices as used in Question 2. How many new trainee staff would be added in January 2013 according to this model? How many probationary staff members will there be at the end of the second month in 2013 according to this model? Express your answer to the nearest whole number.arrow_forwardConsider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1.1 1.7 0.8 0 0 1.3] 0 L= 0 0.6 0 0 0 0 0.2 0 and the initial population distribution is 40 of the first age group, 17 of the second age group, 10 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is x0 = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. λ1 = What is the long-term growth rate of this population of elk as a percent? growth rate = over/under 100%.) Are the elk thriving, static, or going extinct? ? (The growth rate is the percentage of growtharrow_forward2) A researcher theorizes that there is a linear relationship between the number of pets a person owns and their square footage of living space (measured in 1000 of square feet). Answer the questions below with the following data: (1.2,2), (1.1,1), (0.9,3), (1.5,3), (1.45,2), (1.1,2) Set up the matrix that are required to do the calculations: a. b. Calculate b C. Calculate r, R² and what does this tell us? d. Given the ANOVA table, with the test the fit of the model? (note a = 0.05) Source Df SS MS Model 2 28.1987 14.0994 Residual 4 2.8013 0.7003 Total 6 31 Build a 95% confidence interval for b₁ e.arrow_forward
- Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1.1 1.7 1.3 0.8 0 0 0 L = 0 0.6 0 0 0 0 0.2 0 and the initial population distribution is 40 of the first age group, 17 of the second age group, 10 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is xo = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. 11 = What is the long-term growth rate of this population of elk as a percent? growth rate = over/under 100%.) Are the elk thriving, static, or going extinct? ? (The growth rate is the percentage of growtharrow_forwardA car rental service in a certain town has a fleet of about 600 cars, at three locations. A car rented at one location may be returned to any of the three locations. The various fractions of cars returned to the three locations are shown in the matrix to the right. Suppose that on Monday there are 295 cars at the airport (or rented from there), 65 cars at the east side office, and 240 cars at the west side office. What will be the approximate distribution of cars on Wednesday? Cars Rented From: Airport East West 0.95 0.03 0.12 0.00 0.94 0.06 0.05 0.03 0.82 Returned To: Airport East West On Wednesday, 274 cars will be at the airport, 52 cars will be at the East location, and 274 cars will be at the West location. (Round to the nearest integer as needed.)arrow_forwardPlease show complete solutions with explanations. I want to lear how to solve it. Thank you so much for your help! Have a nice dayarrow_forward
- .arrow_forwardIn a certain town, the proportions of voters voting Liberal and Conservative by various age groups is summarized by matrix A, and the population of voters in the town by age group is given by matrix B. Interpret the entries of the matrix product BA. Lib. Cons. Under 30 0.62 0.38 30-50 0.51 0.49 = A Over 50 0.24 0.76 B =[ 2000 Under 30 In the matrix BA, the first entry means that there are voters 8000 1000] 30-50 Over 50 and the second entry means that there are votersarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning