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Let Rz] be the set of all polynomials in variable x Let R(x) be the set of all rational functions over R, that is, R(1) := {p(¹) Note that R[x] R(x) and that R(x) is a field. : p(x), q(x) = R[x], q(x) ‡ 0 (x) #0}. Let A (r) be a 3 x 3 matrix with entires from R(x) given by G -X Dotorming if 4(r) is nonsingular/invertible over R(x), and if so, then find A-¹(x). A(x) = X 2+x -1+x² -3+3x+x² x² -1-x-x³ -2x - x² - 7³

Let Rz] be the set of all polynomials in variable x Let R(x) be the set of all rational functions over R, that is, R(1) := {p(¹) Note that R[x] R(x) and that R(x) is a field. : p(x), q(x) = R[x], q(x) ‡ 0 (x) #0}. Let A (r) be a 3 x 3 matrix with entires from R(x) given by G -X Dotorming if 4(r) is nonsingular/invertible over R(x), and if so, then find A-¹(x). A(x) = X 2+x -1+x² -3+3x+x² x² -1-x-x³ -2x - x² - 7³

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.4: Zeros Of A Polynomial
Problem 1E: 1. Find a monic polynomial of least degree over that has the given numbers as zeros, and a monic...
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Let Rr be the set of all polynomials in variable x Let R(x) be the set of all rational functions over R, that is, R(x) p(x) q(x) Note that R[x] R(x) and that R(x) is a field. A(x) : = Let A(r) be a 3 x 3 matrix with entires from R(x) given by -1 G -X Determine if A(z) is nonsingular/invertible over R(x), and if so, then find A-¹(x). p(x), q(x) = R[x], q(x) ‡ 2(z) #0}. X 2+x −1+x² −3+3x+x² x² -1-x-x³ -2x - x² - ³
Transcribed Image Text:Let Rr be the set of all polynomials in variable x Let R(x) be the set of all rational functions over R, that is, R(x) p(x) q(x) Note that R[x] R(x) and that R(x) is a field. A(x) : = Let A(r) be a 3 x 3 matrix with entires from R(x) given by -1 G -X Determine if A(z) is nonsingular/invertible over R(x), and if so, then find A-¹(x). p(x), q(x) = R[x], q(x) ‡ 2(z) #0}. X 2+x −1+x² −3+3x+x² x² -1-x-x³ -2x - x² - ³
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