Problems 61-70 refer to the following transition matrix
Find the probability of going from state
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- Q.1 Suppose a simple economy with only an agriculture industry and a steel industry with the following technology matrix. Find the gross production of each industry if surpluses of 15 units of agriculture products and 35 units of steel are desired. A S 0.3 0.2 Agrikultwe 0.1 0.4] Steel A =arrow_forward2.2.5. A simple Usher model of a certain organism tracks immature and (.2 3 mature classes, and is given by the matrix P .3 .5 a. On average, how many births are attributed to each adult in a time step? b. What percentage of adults die in each time step? c. Assuming no immature individuals are able to reproduce in a time step, what is the meaning of the upper left entry in P? d. What is the meaning of the lower left entry in P?arrow_forwardNext question Dem. Rep. In a certain town, the proportions of voters voting Democratic and Republican 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. 0.28 0.72 Under 30 0.78 0.22 | = A 30-50 Over 50 0.35 0.65 Interpret the entries of the matrix product BA. | 1000 7000 6000 B = Under 30 30-50 Over 50 In the matrix BA, the first entry means that there are voters and the second entry means that there are votersarrow_forward
- 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_forwardCan someone please help me with these questions. I am having so much trouble. The questions had to be in separate pictures.arrow_forwardThe number of non-zero entries in the adjacency matrix of the given graph is _____ a. 16 b. 10 c. 6 d. 4arrow_forward
- Consider a communication channel where each substation transmits and receive data. The probability between the substations is shown in figure 3. 0.4 0.5 0.3 0.2 2 2 3 0.3 Figure 3 i. Draw a transition diagram. ii. Write down a transition matrix, P. iii. Name the type of matrix in Q3(b) P(X; =2 X,=1\X, =3) iv. P(X; =2 _X,=3{X, =2) V.arrow_forwardOc. O D. The given matrix A not a transition matrix, so there is no diagram. Barrow_forwardConsider a communication channel where each substation transmits and receive data. The probability between the substations is shown in figure 3. 0.4 0.5 0.3 0.2 2 2 0.3 Figure 3 i. Draw a transition diagram. ii. Write down a transition matrix, P. iii. Name the type of matrix in Q3(b) P(X, =2 X, = 1|X, =3) iv. P(X, =2 X, = 3X, =2) V. enarrow_forward
- 6. Q.1: If matrix A =| Find a formula for Ak %3D 2 3arrow_forward*Use the following scenario for questions 5-8. Jennie and her friends go off campus everyday for lunch; they choose between three restaurants each day to go to: Cook-out, McDonald's, and Taco Bell. They never go to the same restaurant two days in a row. Below is the given transition matrix: LA 23 yesterday? A. 0.50 24 Monday? A. 0.00 25 A. 0.31 26 W www PROCURA A. Taco Bell B. 0.40 B. What is the probability that Jennie and her friends choose to go to Cook-out when they went to McDonald's 0.27 CMT COSA B. 0.32 C. 0.60 What is the probability that Jennie and her friends will go to Taco Bell on Thursday after they went to Taco Bell on B. Cook-out CMT 0.3 7 C. 0.58 .5 0.5 0 4 C. 0.37 In the long run, what percentage of the time does Jennie and her friends visit McDonald's? D. 0.30 Which restaurant does Jennie and friends frequent the most? C. McDonald's D. 0.42 D. 0.90 D. None of these restaurants Sign ouarrow_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_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning