Explanation of Solution
Infinite number of solutions:
Consider the following linear system,
Where
This system can be written as given below:
Therefore, we have,
We know that the transpose of the matrix does not affect the rank of the matrix.
Therefore, we get
Adding all the rows in the last row will give
Trending nowThis is a popular solution!
Chapter 2 Solutions
Student Suite Cd-rom For Winston's Operations Research: Applications And Algorithms
- The Legendre Polynomials are a sequence of polynomials with applications in numerical analysis. They can be defined by the following recurrence relation: for any natural number n > 1. Po(x) = 1, P₁(x) = x, Pn(x) = − ((2n − 1)x Pn-1(x) — (n − 1) Pn-2(x)), n Write a function P(n,x) that returns the value of the nth Legendre polynomial evaluated at the point x. Hint: It may be helpful to define P(n,x) recursively.arrow_forwardFind the relation between the following functions: f(n) = log n and g(n) = Vn. (Square root for n)Hint: you may use L'Hopital's Theorem. For function f(n)=log n and time t=1 second, determine the largest size n of a problem that can be solved in time t, assume that the algorithm to solve the problem takes f(n) microseconds. Suppose you have algorithms with the two running times listed below. Suppose you have a computer that can perform 6 operations per second, and you need to compute a result in at most an hour of computation. For each of the algorithms, what is the largest input size n for which you would be able toget the result within an hour for:a) n^3b)10n^2arrow_forwardFor each set of cubes in terms of variables (a, b, c, d] obtain the minimized version for boolean fuction f(a, b, c, d) (00X1, 0XX1, 1000, 1100, 1010, 1110} {1XX0, 10XX, 11XX, 00XX} ✓ {00XX, 01XX, 0XXX, 01X1} (0100, 1010, 1XX1, XXXX, 0001} {0001, 0011, 0101, 0111, 1101, 1111, 1001, 1011} ✓ {000X, 010X, 1X00, 1X01} A f(a, b, c, d) = 1 B. f(a, b, c, d) = d C. f(a, b, c, d) = ē D. f(a, b, c, d) = a + a b Ef(a, b, c, d) = a F. f(a, b, c, d) = a darrow_forward
- H.W:- D. Consider f(x) = x + 3x - 5, where [a = 1, b= 2] and s-0.001.arrow_forwardDetermine φ (m), for m=12,15, 26, according to the definition: Check for each positive integer n smaller m whether gcd(n,m) = 1. (You do not have to apply Euclid’s algorithm.)arrow_forwardLet f (n) and g(n) be positive functions (for any n they give positive values) and f (n) = O(g(n)).Prove or disprove the following statement:arrow_forward
- 6. Suppose functions f(n) > 0 and g(n) > 0 satisfy f(n) = 0(9(n)). Prove or give a counterexample to each of the following. (a) log, f(n) = O(log, 9(n)). To avoid an obscure special case, assume that g(n) > 2 for all n. (b) 2/(n) = 0(29(n)) %3D %3D (c) (f(n))² = 0(g(n))")arrow_forwardLet N = {0, 1, 2, . . .} be the set of Natural Numbers. Given an n ∈ N, which of the followingconditions are necessary, and which of these conditions are sufficient, for the Natural Number,n, to be a factor of 10.(a) 1 is a factor of n.(b) 1 is a factor of 2n.(c) −n is a factor of 10.(d) 10 is a multiple of n.(e) n is divisible by 2.(f) n^2 is divisible of 5.(g) n = 10.arrow_forwardIf S = { x | 0 ≤ x ≤ 10}, A = { x | 1 ≤ x ≤ 5}, B = { x | 1 ≤ x ≤ 6}, and C = { x | 2 ≤ x ≤ 7}(a) S ⋃ C(b) A ⋃ B(d) A’ ⋂ C(c) A’⋃ (B ⋂ C)(e) (A ⋂ B) ⋃ (B ⋂ C) ⋃ (C ⋂ A)arrow_forward
- Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
- C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education