Suppose that K is an extension field of F with a, B,y E K Prove that if {a, B, 7} is linearly independent over F, then {a+B,a – Y, ß – v} is linearly independent over F.
Suppose that K is an extension field of F with a, B,y E K Prove that if {a, B, 7} is linearly independent over F, then {a+B,a – Y, ß – v} is linearly independent over F.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 17E: Suppose that f(x),g(x), and h(x) are polynomials over the field F, each of which has positive...
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![Suppose that K is an extension field of F with a, B,y EK Prove that
if {a, B,7} is linearly independent over F, then {a + B, a – Y, ß – 7} is
linearly independent over F.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbad2ff6b-2d7b-4eb4-8aaa-43d505b53172%2Fad932bad-72cb-4183-8836-c23e0d2fc769%2Fo38rdo_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that K is an extension field of F with a, B,y EK Prove that
if {a, B,7} is linearly independent over F, then {a + B, a – Y, ß – 7} is
linearly independent over F.
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