(i.e. running the Euclidean algorithm backwards), find the general solution to each of the following:
(i.e. running the Euclidean algorithm backwards), find the general solution to each of the following: We...
PROBLEM 1 For each of the following pairs of integers, use the Euclidean Algorithm to find ged(a,b), and to write gcd(a,b) as a linear combination of a and b, i.e. find integers m and n such that gcd(a,b) = am + bn. (a) a = 36, b = 60. (b) a = 12628, b = 21361. (c) a = 901, b = -935. (d) a = 72, b = 714. (e) a = -36, b = -60.
Use the reduction of order method to find the general solution of each of the following equations. One solution of the homogeneous equation is shown alongside each equation. We were unable to transcribe this image
a Find the greatest common divisor (gcd) of 322 and 196 by using the Euclidean Algorithm. gcd- By working back in the Euclidean Algorithm, express the gcd in the form 322m196n where m and n are integers b) c) Decide which of the following equations have integer solutions. (i) 322z +196y 42 ii) 322z +196y-57
How do i find the transfer function for the following Laplace transform... i.e... We were unable to transcribe this imageWe were unable to transcribe this image
Since are solutions of the associated homogeneous equation, find the general solution of the differential equation using the parameter variation method. Write the system of equations and use Cramer's rule to find the solution. We were unable to transcribe this imageWe were unable to transcribe this image
We discuss the Euclidean algorithm that finds the greatest common divisor of 2 numbers u and v. We want to extend and compute the gcd of n integers gcd(u1,u2,….un). One way to do it is to assume all numbers are non-negative, so if only one of if uj≠0 it is the gcd. Otherwise replace uk by uk mod uj for all k≠j where uj is the minimum of the non-zero elements (u’s). The algorithm can be made significantly faster if one...
We discuss the Euclidean algorithm that finds the greatest common divisor of 2 numbers u and v. We want to extend and compute the gcd of n integers gcd(u_1,u_2,….u_n). One way to do it is to assume all numbers are non-negative, so if only one of if u_j≠0 it is the gcd. Otherwise replace u_k by u_k mod u_j for all k≠j where u_j is the minimum of the non-zero elements (u’s). The algorithm can be made significantly faster if...
Let V be a Hilbert space. Let S1 and S2 be two hyperplanes in V defined by Let be given. We consider the projection of y onto , i.e., the solution of (1) (a) Prove that is a plane, i.e., if , then for any . (b) Prove that z is a solution of (1) if and only if and (2) (c) Find an explicit solution of (1). ( d) Prove the solution found in part (c) is unique. We...
Using matrix For problems 5 and 6, use variation of parameters to find the general solution with A and G given. Alse satisfy the initial value problem. We were unable to transcribe this image
Suppose is a directed graph represented by a adjacency lists. Divise a linear time algorithm that, given such a , returns a list of all the source vertices of . (Note, this list may be empty.) Prove your algorithm runs in -time. Hint: There is a simple solution that does not involve any DFS’s or BFS’s. G (V. E) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image