The extended Euclidean algorithm computesthe gcd of two integers ro and r₁ as a linearcombination of the inputs.gcd(ro, r₁) = s.ro + t •rıHere s and t are integers known as the Bezoutcoefficients. They are not unique.The algorithm works like the standard Euclideanalgorithm, except that at each stage the currentremainderri is expressed as a linear combination of theinputs.ri = siro + tir₁.This produces a sequence of numbersTo, T1,Tn-1, Tn where r = 0 andgcd(ro, r₁) = Tn-1. Suppose that ro = 420 andT1 = 382.Give the sequence ro, T1,..., Tn-1, în in the blankbelow. Enter your answer as a comma separated list ofnumbers.What is GCD(420,382)?What is s?What is t?

Given Information:The numbers are given as and .Objective:Find the of and by Euclidean Algorithm.…

The extended Euclidean algorithm computes the gcd of two integers ro and r₁ as a linear combination of the inputs. gcd(ro, r₁) = Here s and t are integers known as the Bezout coefficients. They are not unique. = s · ro + t · r₁ The algorithm works like the standard Euclidean algorithm, except that at each stage the current remainder î¿ is expressed as a linear combination of the inputs. rį = sįro + t¿r₁. = This produces a sequence of numbers To, 1,,Tn-1, n where n 0 and gcd(ro, r₁) = Tn-1. Suppose that ro T₁ = 382. What is GCD(420,382)? What is s? Give the sequence ro, T1,..., Tn-1, în in the blank below. Enter your answer as a comma separated list of numbers. What is t? = 420 and

The extended Euclidean algorithm computes the gcd of two integers ro and r₁ as a linear combination of the inputs. gcd(ro, r₁) = Here s and t are integers known as the Bezout coefficients. They are not unique. = s · ro + t · r₁ The algorithm works like the standard Euclidean algorithm, except that at each stage the current remainder î¿ is expressed as a linear combination of the inputs. rį = sįro + t¿r₁. = This produces a sequence of numbers To, 1,,Tn-1, n where n 0 and gcd(ro, r₁) = Tn-1. Suppose that ro T₁ = 382. What is GCD(420,382)? What is s? Give the sequence ro, T1,..., Tn-1, în in the blank below. Enter your answer as a comma separated list of numbers. What is t? = 420 and

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 2CEXP

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