PRACTICE EXERCISE 2.4 If A = 3a, + 2a 6a and B (a) A B - = 4a,3a, determine (b) A X B (c) The vector component of A along a, at (1, 7/3, 57/4)
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- 1. Create a K-map for each of the following functions: i. X1 X2| f 0 0 1 1 1 0 1 1 1 ii. f (x1,x2, x3) = Em (1,2, 3, 7) Ση (1,2, 3, 7) iii. f (x1, x2, X3) = x1· X2 + x2· X3 X2 + X2 · X3a. Build an adjacency matrix ? for this map. b. How many paths of length 2 from V5 to V1 exist? c. How many paths of length 3 from V5 to V1 exist?1. Implement a helper function called rref pp (A, b) that applies Gaussian Elimination with partial pivoting to return the Reduced-Row Echelon Form of the augmented matrix formed from Matrix object A and Vec object b. The output must be of the type Matrix. 2. Implement the function solve pp(A, b) that uses rref pp (A, b) to solve the system A = b. The input A is of the type Matrix and b is of the type vec. o If the system has a unique solution, it returns the solution as a Vec object. o If the system has no solution, it returns None. o If the system has infinitely many solutions, it returns the number of free variables (int) in the solution. def _rref_pp(A, b): # todo pass def solve_pp(A, b): #todo pass Python
- Q.1)Consider a system with 6 processes P1, P2, P3, P4, P5 and P6 who are requesting 4 resource types – A, B,C and D at the same time. The following snapshot of the system has been given at the moment.Process Maximum Allocation AvailableA B C D A B C D A B C DP1 4 2 1 2 2 0 0 1 3 3 2 1P2 5 2 5 2 3 1 2 1P3 2 3 1 6 2 1 0 3P4 1 4 2 4 1 3 1 2P5 3 6 6 5 1 4 3 2P6 4 2 3 5 1 0 2 2A) Compute the Need Matrix for the above data. (4 points)B)Is the system in a safe state? Why? If yes, show the safe sequence. Kindly show each and every step ofyour solution. (8 points)C)Now, if a request from process P2 arrives for (1,1,0,1), should the request be granted immediately? Whyor Why not? Kindly show each and every step of your solution. (8 points)Return co-ordinate 1 from (vector 3 1 4 2). In Racket1(a). For an M/M/1 queuing system, write your own function in R to compute andoutput the:1. long-run probability po,p1,…,pn of there being 0,..,n people in the system.2. the values L, Lq, W, Wq, and Wse. The function should return elements with the names probs (vector of po,…,pn), L, Lq, W,Wq, and Wse (does not have to be in this order) The function should take as inputs, lambda (arrival rate), mu (service rate), and n (thenumber of people to compute probabilities for 0,…,n) Note: you are to code the computations for the above on your own, so none of the functionsin the queueing package are to be used. 1(b). Using your function from 1(a), find the values (b)-(f) in the Queuing Theory(M_M_1).
- Q3/ Give A B and AB for the following set ( 0 ° 0 0 0 1 1 1 0 1 1 1 0 1 1 1 O ° 0 0 O O 0 0 Input matrix Structuring elementSuppose we have a two-dimensional vector [ U₁ U₂]. Select all the translations that would occur on the vector from the operation [ u₁, U2 ]-[-7, -5] 2 O Shift up Shift down Shift right Shift left O No horizontal shift No vertical shiftAlgorithm to Determining an orbit and Schreier vectorInput : a set S = {s 1, s2 ..... Sm} of generators of a group G acting on f2; a point 5;Output : the orbit ~G; a Schreier vector v and backward pointers w of the orbit 8 G relative to the set S of generators;